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ADVERTISEMENT. 



Geldaed's TTats-d-book on Cotton Manufacture, designed 
for the use of Millwrights, Managers, Overseers, Operatives, 
and builders of Cotton and other Machinery. Contain- 
ing rules and examples for finding the speed and dimen- 
sions of all the wheels and pulleys necessary for Mill 
Gearing, the wheels, pulleys, rollers, etc., etc., neces- 
sary to produce any desired result at each and every ope- 
ration in a cotton mill, by an original and comprehen- 
sive system of calculations, deduced from Algebra and 
other sources, so simplified as to come within the compre- 
hension of all who are acquainted with the fundamental 
rules of common arithmetic. 

Rules and examples for finding {at one operation) all 
the necessary draughts, t.wist, doublings, and allowance 
for loss in working, to produce any given number of yarn. 

Rules and examples for finding the weight and number 
of yarn, and the necessary allowance for waste and shrink- 
age in weaving, to produce any given kind of cloth. 

Rules and examples for finding the number of yards of 
cloth per pound, and the proper price to pay for weaving 
any given kind of cloth. 

Compendious tables adapted to the new system of 



11 ADVEKTISEMENT. 

weighing sliver, roving, and yarn, in the manufacture of 
cotton, wool, and flax. 

All of which are entirely original, and exemplified in a 
more brief and comprehensive manner than has ever 
before been published. Calculated and arranged during 
thirty-seven years of practical experience in the various 
branches of Cotton Manufacture, by James Geldakd, 
Lonsdale, K. I. 

Illustrated by engravings of the most approved ma- 
chinery, which is now being adopted in all first-class 
mills. 

Complete in one volume, 12mo. Price $2.50. 

Published and for sale by John "Wiley & Son, 535 
Broadway, New York. 

*^* Will be sent free, by mail, on receipt of price. 




j 



r^ 



iti^ 



HA.NID-BOOK 



ON 



COTTON MANUFACTURE 



OB, 



A. GUJIDE TO 



MACHmE-BUILDmG, SPIMmG AND WEAVING; 



WITH PRACTICAL EXAMPLES, ALL NEEDFUL CALCULATIONS, AND MANY USEFUL 
AND IMPORTANT TABLES: THE WHOLE INTENDED TO BE A COM- 
PLETE YET COMPACT AUTHORITY FOR THE MANU- 
FACTURE OP COTTON. 



By JAMES GELDAKD, 







LONE 


jDALE, 


K. I. 


y of Co.- 

~i 

'Wash. 




c^ 


NEW YOKK : 




JOHN 


WILEY & 


SON, 


535 


BROAT^WAY 








1867. 












v/ 







X 



/ 

/ 



Entered according to Act of Congress, in the year 1867, by 

JOHN WILEY k SON, 

In the Clerk's Office of the District Court of the United States for the Southern 

District of New York. 



The New York Printing Company, 
8 1, 83, and 85 Centre Si., 

NEW YORK. 



1" ' 



i 



PREFACE. 



The utility of a suitable hand-book on Cotton Manufac- 
ture — which has become so important a branch of our 
national industry — can scarcely be a matter of question. 

Several works have been published on the subject, both 
in this country and in England, each one of which has its 
peculiar merits : it may, perhaps, seem presumptuous in 
the author to add this to the number. All he asks, how- 
ever, is that the judicious reader shall examine his pages, 
and decide for liimself upon the value of their contents. 

The work is designed especially for the Cotton Manu- 
facturer, but it is hoped that it will be found useful to 
manufacturers of woollen and linen goods, to builders of 
machinery, to the general mechanic, and to the student 
intending to prosecute any branch of manufacture in 
which machinery is used. 

The plan of the work is — 

First. To make all necessary calculations as to the 
dimensions of the Mill Gearing, and the machinery to be 
employed. 

Second. To introduce the cotton and show at a glance 
the draughts, and doublings, and necessary allowance for 
loss in working, to produce any required result. The 
author has had familiar acquaintance with the hest of 



VI PKEFAOE. 

modem machines, American and English, and has based 
his calculations upon those most recently adopted in our 
first-class mills. 

Some of the examples may seem to contain needless 
repetitions, but it is thought best that every feature of the 
statement should appear in each problem, in order that 
the whole may be seen and comprehended at once. The 
system of cancellation adopted will be found so ready an 
offset to these repetitions that, as will be seen, they can 
be easily afforded. 

The work is entirely original, and although conceived 
amidst the noise of labor, and written in hours stolen 
from rest, the author has confidence in its theoretical and 
practical accuracy, and gladly stakes his reputation upon 
its success. 

The author desires thus publicly to express his grateful 
acknowledgments for the kindness of Prof. B. F. Clark, 
of Brown University, who has encouraged him by pro- 
nouncing his manual mathematically correct. 



INDEX. 



Mill Gearing. 

PAGB 

Remarks on mill gearing, . .11 

To find a train of wheels, etc., etc., to produce a given speed, . 12 

Remarks on finding proper wheels, 13 

Remarks on rule for placing the terms, 14 

Mixing Cotton, . . . 17 

The Willow, 18 

Lappee. 

Remarks on lapper, .19 

To find a train of wheels, rollers, etc., etc., to produce a given 
draught, ........... 23 

To find the draught, 27 

Intermediate draughts, ........ 29 

To find a train of wheels and pulleys to produce a given veloc- 
ity of the circumference of the fan, . . . . .33 

To find the velocity of the circumference of the fan, . . ,36 

Carding Engine. 

To find a train of wheels and pulleys to produce a given speed 

of the main-cylinder, . . . . ' . . . .38 
To find the speed of the main-cylinder, . . . . .39 
To find a train of wheels to connect the main-cylinder with the 

dof&ng-cylindcr, ......... 41 

To find a train of wheels, pulleys, etc., etc., to connect the dofi"- 

ing-cylinder and the railway-head, . . . . .43 

To find the draught {or gain) between the dofiing-cyhnder and 

the railway-head, ......... 46 

To find a train of wheels to connect the doffing-cylinder and the 

feed-roller, 47 

To find the total draught of the card, 48 



O INDKX. 

Rail way-Head. 

FAGB 

To find a train of wheels and cones to produce a given draught, 52 

To find the draught, . . . , 55 

To find the intermediate draughts, 57 

To find a train of wheels to produce a given ratio of velocity to 

the delivering balls and can, ....... 63 

To find the ratio of velocity of the can to that of the delivering- 

balls, 65 

To find a train of wheels to produce the draught, . . .68 

To find the draught, 69 

Bobbin and Fly-Frame. 

To find a train of wheels to connect the first driven shaft and the 

spii:^dle, 72 

To find the revolutions per minute of the spindle, . . .74 

Remarks on the differential coupling, 75 

To find a train of wheels to connect the external wheel with the 

bobbin, 76 

To find the revolutions per minute of the bobbin, . . .78 
To find a train of wheels to connect the first driven shaft and the 

front roller, 79 

To find the revolutions per minute of the front roller, . . 80 

To find the twist per inch of roving, ...... 81 

To find the revolutions per minute of the external wheel, . . 84 
To find how many revolutions per minute the external wheel 

and the bobbin have been retarded, . . . . .85 

To find a train of wheels, pulley, and cone, to connect the first 

driven shaft with the differential- wheel, 87 

To find the revolutions per minute of the differential-wheel, . 89 
To find a train of wheels and rollers to produce the draught, . 94 

To find the draught, 95 

Intermediate draughts, 97 

To find a train of wheels to produce a given length of traverse to 

the capping-rail, ......... 101 

Spinning Frame. 

To find the diameter of the cylinder, 109 

To iind a train of wheels and pulleys to connect the front roller 

and the cylinder, . . . . . . . . .110 

To find the revolutions per minute of the front roller, . . Ill 

To find the tAvist per inch of yarn, . . . . . .112 

To find a train of wheels and pulleys to connect the front roller 

with the heart or traverse motion, 114 



INDEX. y 

Mason's Mule. 

PAGE 

To find a train of wheels and pulleys to drive the mule a given 
number of stretches per minute, ...... 119 

To find the tAvist per inch of yarn, ...... 122 

To find a train of wheels to connect the front roller and the car- 
riage, 124 

To find a train of wheels, pulleys, etc., etc., to pass from the car- 
riage-chain through the mule-head to the spindle, to give the 
bare spindle a surface velocity equal to the traverse of the car- 
riage while going in, 127 

To find a train of wheels, etc., etc., for the builder to make a cop 
containing a given number of stretches, .... 135 

To find the length of cop, 137 

To find a train of wheels and rollers to produce the draught . 189 
To find the draught, 141 

Franklin Mule. 

To find a train of wheels, pulleys, etc., etc., to produce a given 
quantity of twist per inch of yarn, ..... 146 

To find the twist per inch of yarn, 148 

To find a train of wheels to connect the twist-shaft and the 
front roller, 150 

To find a train of wheels to give the front roller and the draw- 
ing-out scroll equal surface velocities, ..... 153 

To find a train of wheels to give the winding-on drum, and bare 
spindle, equal surface velocities, when winding on the first 
stretch, 157 

To find the surface velocity of the bare spindle, when winding on 
the first stretch, 1.59 

Dressing Machines. 

To find a train of wheels and cones to produce a given surface 
velocity of the empty beam, 164 

To find a train of wheels and pulleys, to produce a given velocity 
of the circumference of the fan, 169 

To find the diameter of the neck-roller to produce a given length 
of cut 173 

Power Loom. 

To find a train of wheels and emery roller, to ^^ut in a given 
number of picks per inch, ....... 177 

To find a train of wheels to make the let-off motion correspond 
with the take-up motion, 185 



10 lA^DEX. 

PART II. 

Carding. 

PAOB 

Examples explanatory of the yarn, roving, and sliver tables, . 193 
To find the decimal of a hank spread on the lattice, . . 198 

To find the draughts, doublings, and necessary allovsrance for loss 

in working, to produce any given number, .... 199 
To find the number produced at each and every operation, from 
the weight spread on the lattice, and from the number pro- 
duced, "" 208 to 219 

Loss in working, ......... 222 

To find the speed of a railway-head, drawing-frame, etc., etc., to 
supply a given number of mule spindles, . . 225 to 232 

Spinning. 

To find a train of wheels, rollers, etc., etc., to produce a given 

draught, 233 to 248 

To find the product per spindle, and spinners' wages, . . 249 
To find the twist per inch of yarn 250 

Manufacturing. 

To find the number of hanlvs of warp and filling to make a given 
number of cuts, ......... 255 

To find the number of yards of cloth per pound, . . . 257 
To find the time it will take a loom to weave a given quantity of 

cloth, 273 

To find the percentage of power utihzed by a loom, . . 273 

To find the monthly wages of a weaver, 275 

To find the proper price to pa}' for weaving, . . ' . . 276 
To find the proper amount of wages, to ad-\'ance the several kinds 

of cloth, . ■ 278 

Sliver table, 281 

Roving table, 284 

Yarn table, 285 

Reed table, 288 

Linen yarn table, ......... 292 

Woollen vara table, 295 

Remarks on Draper's Patent Evener, 296 

Evener tallies 297 



LIST OF ILLUSTEATIONS 



PAOB 

DoDGEViLLE Frontispiece. 

Corliss' Steam Engine 12 

Whitin's Improved Lapper 19 

Whitin's Carding Engine '. 37 

Draper's Eailway Head . ' 50 

Brown's Patent Speeder 70 

Fales' and Jenks' Spinning Frame 107 

Franklin Mule 142 

Social Mill , . 191 

Clinton Mill 233 

Androscoggin Mill 255 



HAND-BOOK 



COTTON MANUFACTURE. 



PART I. 

MILL-GEARING. 



Mechaniciajsts have always disagreed as to the best mode 
of conveying power from the prime mover to the ma- 
chinery to be unpolled. Some prefer gearing, some belts 
and pulleys, while others prefer a mixture of both. 
Doubtless each system has its advantages. All agree, 
that, to convey the power by the shortest possible train, 
first to the heaviest and then the lighter machinery, is 
correct both in theory and practice. 

Whatever system is adopted, the mode of finding the 
proper gears, pulleys, speed, etc., etc., is substantially 
the same. 

Many prefer very light, well-balanced pulleys and 
shafting, and counter-balance the want of weight and 



12 



COTTON MANIJFACTTIRE. 



strength by having a small driven wheel or pulley near 
the prime mover, and small driving pulleys near the 
machinery to be impelled, which gives a proportionately 
increased velocity to produce the same momentum. This 
system greatly reduces the inertia to be overcome, and 
tends to more uniform impulsion and utility of the power 
applied. 

A steam-engine makes 50 double strokes per minute, 
and drives an upright shaft 180 revolutions per minute 
by a train of two pairs of wheels ; the driving wheels 
have respectively 210 and 54 teeth. 

Required, the number of teeth respectively in the two 
driven wheels. 



Revolutions per minute 
of the upright shaft, 180 



50 Double strokes per mi- 
nute of the steam- 
engine. 
210 Teeth in the first diiv- 
ing wheel, 

54 Teeth in the second 
di'iving wheel. 



Worked Out. 



l-2-18(0 



5(0 
210 
54-6-3 



{Continued^ 



5 'Pi 



^ > m 




MLLL-GEAErSTG. 13 

210 

5 



1050 
3 



B . . . . 10)3150 



B . . . . 5)315 

A . . . 63)63 

1 

A. 63 = 63 Teeth in tlie first driven wheel. 

B. 10 X 5 = 50 Teeth in the second driven wheel. 

Answer. 

!N^.B. — It will be perceived, by a little reflection, that 
the driven wheels are found by first dividing the product 
of the double strokes per minute of the steam-engine, and 
the number of teeth in the driving wheels by the revolu- 
tions per minute of the upright shaft, and the quotient 
by as many numbers as will divide without a remainder. 
The last divisors are classed according to the number 
and size of wheels required, which is dictated by location 
and other circumstances. The product of the numbers 
in each class gives the respective wheels. 

From the particulars found in the preceding example, 
find the revolutions per minute of the upright shaft. 



14 



COTTON MANUFACTURE. 



Teeth in the first driven 
wheel 63 

Teeth in the second driv- 
en wheel 50 



60 Double strokes per mi- 
nute of the steam- 
engine. 
210 Teeth in the first di'iv- 
ing wheel. 

.54 Teeth in the second 
driving wheel. 



Worked out hy Ccmcellation. 






504 




l-T-63 


210-30 




1-50 


54-6 




30 X 6 


= 180 


Answer. 



Hie sa/me without Ccmcellation. 
Dividend . . 50 x 210 x 54 
Divisor ... 63 x 50 



= 180 



Answer. 



l^.B, — The product of all the terms on the left-hand 
side of the perpendicular line into the answer will equal 
the product of all the terms on the right-hand side of this 
line. Thus : 63 x 50 x 180=567000 ; 210 x 54 x 50 = 
567000. Hence we have the following rule to find any 
of the above terms : Place all the terms classed with the 
one sought on the left-hand side, for a divisor (less the 
term sought), and all the rest on the right-hand side for a 



MILL-GEAEING. 15 

dividend, and proceed by cancellation or multiplication : 
divide the product of the terms on the right-hand side by 
the product of the terms on the left-hand side, and the 
quotient will be the answer. This rule applies to all 
problems of this nature. 

From the particulars found in the preceding example, 
find the number of teeth in the driven wheels. 



Wo7'ked out hy Cancellation. 
504 
21(0 



1-248(0 
1-50 



54:-6-3 



21 X 3 = 63 Teeth in the first driven wheel. 

Answer. 

The same without Ca/ncellation. 
Dividend . . . 50 x 210 x 54 no 

= DO. 

Divisor .... 180 x 50 

Answer. 

Worked out hy CoMcellation. 



1-348(0 
l-Y-63 



5(0 

210-30-10 

54-6-1 



10 X 5 = 50 Teeth in the second driven wheel. 

Answer. 



IG COTTON MA]SniFACTlIRE, 

The sa/me without Cancellation. 

Dividend . . . 50 x 210 x 54 ^ ^^ 

Divisor .... 180 x 63 

Answer. 

From the particulars found in the preceding example, 
find the double strokes per minute of the steam-engine, 
and the number of teeth in the driving wheels. 



Worhed out hy CamjCellation. 




180-20-10 


1-21(0 


63-3-1 


1-2-6-54 


5(0 



10 X 5 = 50 Double strokes per minute of the steam- 
engine. 

Answer. 

The same without Cancellation. 

Dividend . . . 180 x 63 x 50 ^^ 

— = 50. 

Divisor .... 210 x 54 

Answer. 

Worked out l)y Cancellation. 



1-50 
1-6-54 



180-30 

63-7 

50-1 



30 X 7 210 Teeth in the first driving wheel. 

Answer. 



MILL-GEAEESTG. 17 

TTie same without Ca/ncellation. 
Dividend . . . 180 x 63 x 50 ^ ^lo 

Divisor .... 54 x 50 

Answer. 

Worked out hy Cancellation. 



1-50 


18(0 


1-21(0 


63-3 




50-1 



18 X 3 == 54 Teeth in the second driving wheel. 



Answer. 

The same without Ca/ncellation. 

Dividend . . . 180 x 63 x 50 k. 
= 54. 

Divisor .... 210 x 50 

Answer. 



MIXING COTTON. 

To mix together different qualities of cotton, so as to 
get the best possible combination for the purpose of mak- 
ing any given kind of yarn at the least possible expense, 
is an art of the very greatest importance. 

The way of mixing cotton most commonly practised is 
to take as many bales as the mixing-room will conveni- 
ently hold, and 8j)read them in layers on the top of each 



18 COTTON MANUFACTURE. 

other, covering as large an area as tlie room will admit of. 
It is taken from top to bottom of the pile with a rake 
when wanted for use. 

Some cotton-spinners obtain the best results by keep- 
ing the different qualities of cotton separate until they 
have passed through the cards, a system that has many 
arguments in its favor. 

It is the most practicable way to make good, even 
yarn, to use one kind of cotton only, but this is not always 
the cheapest way; hence arises the necessity of mixing 
cottons. 

Suppose a mill to consume 40 bales of cotton per week, 
each weighing 500 pounds, one half at 42 cents, and the 
other half at 36 cents per pound : the total cost of cotton 
per week would be $T,800, while, if the whole was at 42 
cents per pound, the cost per week would be $8,400, a 
difference of $600 per week, or $100 per day, in favor 
of mixing. 

THE WILLOW. 

The Willow is the first machine to which the cotton is 
subjected in its process of manufacture. 

The cylinder of a Bacon-Willow contains 1036 claws, 
and makes 500 revolutions, more or less, while the feed- 
rollers feed one pound of cotton, displaying 1036 x 500, 
518000, claws in rapid motion. These tease the 



THE WILLOW. 19 

cotton into as many loose tufts, and, as far as is practica- 
ble, undo what has been done for convenience in transpor- 
tation, free it from a superabundance of moisture and 
other impurities, and by the force of wind, created by the 
motion of the cylinder, carry it into a ventilated room 
convenient to the lapper. 



THE LAP PEE. 

As will subsequently be shown, the lapper is the 
machine at which the cotton first receives definite form 
and size. 

Some manufacturers contend tliat the size or decimal 
of a hank produced at a lapper cannot be depended upon 
as being positive ; that at best it is but an approximation 
and guess at the quantity of cotton spread on to the lat- 
tice, substituting an "evener" for the old system of 
spreading a definite weight on to a definite length. 

The Whiting Lapper is the one most generally appre- 
ciated in this neighborhood; being easy to manage, not 
liable to get out of order, and, with proper weighing, pro- 
duces good and truthful results, 

A lapper has three beaters. The first one makes 1800, 
the second 2000, and the third 2200 revolutions per 
minute. They are driven from an upright shaft, making 
180 revolutions per minute by a train of tliree pairs of 



20 



COTTON MANTTFAOTUKE. 



pulleys, and one pair of wheels. The driving wheel has 
96 teeth, and the respective diameters of the driving pul- 
leys are 40, 32, and 20 inches. How many teeth should 
there be in the driven wheel, and what should be the 
respective diameters of the driven pulleys, to drive the 
first beater at the speed above named? 



Revolutions per minute 
of the first beater, 1800 



180 Revolutions per minute 
of the upright shaft. 

96 Teeth in the driving 
wheel. 

40, Diameter of the first 
driving pulley in inch- 
es. 

32, Diameter of the second 
driving pulley in inch- 
es. 

20, Diameter of the third 
driving pulley in inch- 
es. 



Worked out. 

148(00 18(0-1 

96 

4(0 

32 

20 

{Continued^ 







IHE LAPPER. 


96 
4 


384 
32 


768 
1152 


12288 
20 


A . 




. . 2)245760 


A . 






. 2)122880 


A . 






. 2)61440 


A . 






. 2)30720 


A . 






2)15360 


A . 






2)7680 


B 






2)3840 


B 






2)1920 


B 






2)960 


B 






2)480 


B 






2)240 


C . 






2)120 


C . 

{Cont 


mv 


ed. 


2)60 



21 



22 COITON MANUFACTURE. 



D . . 


2)30 


D . . 


3)15 


• • • 


5)5 




1 



A. 2x2x2x2x2x2 = 64 Teeth in the 
driven wheel, 

B. 2x2x2x2x2 = 32, Diameter of the first 
driven pulley in inches. 

C. 2x2x5 = 20, Diameter of the second di-iven 
pulley in inches. 

D. 2x3 6, Diameter of the third driven pulley 

in inches, which is on the same axis with the first beater. 

Answer. 

The first beater of a lapper is driven fi'om an upright 
shaft making 180 revolutions per minute by a train of 
three pairs of pulleys and one pair of wheels. The driv- 
ing wheel has 96, and the driven wheel 64, teeth. The 
respective diameters of the di'iving pulleys are 40, 32, 
and 20, and of the di-iven pulleys, 32, 20, and 6, inches. 
How many revolutions per minute does the first beater 
make ? 

180 Eevolutions per minute 
of the upright shaft. 
Teeth in the driven 

wheel 64 wheel. 



96 Teeth in the driving 



THE LAPPEE. 



23 



Diameter of the first 
driven puUej in inch- 
es 

Diameter of the second 
driven pulley in inch- 
es 

Diameter of the third 
driven pnlley in inch- 
es 



32 



20 



40, Diameter of the first 
driving pulley in inch- 
es. 

32, Diameter of the second 
diiving pulley in inch- 
es. 

20, Diameter of the third 
driving pulley in inch- 
es. 



Worked out hy GrniGellation. 
180 

9646-1 
40-10 
324 
204 



4-64 


1-32 


1-20 


1-6 



180 X 10 



1800 



The srnne without Ccmcellation. 
Dividend . 180 x 96 x 40 x 32 x 20 
Divisor . . 



Answer. 



= 1800 



64 X 32 X 20 X 6 



Answer. 



The lattice-roller and lattice are, in effect, equal to a 
roller 4 inches in diameter. On the same axis with the 



24 COTTON MANTJTAOTUEE. 

lattice-roller, there is a wheel that takes into a wheel with 
9 teeth, on the feed-roller. On the feed-roller there is 
also a wheel that takes into a wheel with 42 teeth, on the 
under shaft. On the other end of the under shaft there is 
a wheel that takes into a wheel with 32 teeth, on the side- 
shaft. On the other end of the side-shaft there is a wheel 
that takes into a wheel with 32 teeth, on the clutch-shaft. 
On the clutch-shaft there is also a wheel that takes into a 
wheel with 100 teeth, on the calender-roller. On the 
other end of the calender-roller there is a wheel that 
takes into a wheel with 26 teeth, on the lap-roller. Sup- 
pose the wheels that have their dimensions given above 
to be driving wheels, what should be the dimensions of. 
the driven wheels and the lap-roller to produce a draught 
of 3? 

N.B. — The intermediate wheels are not taken into 
account in the above. 



4, Diameter of the lattice- 
roller, including lat- 
tice, in inches. 
9 Teeth in the wheel on 
the feed-roller. 
42 Teeth in the wheel on 

the under shaft. 
32 Teeth in the wheel on 
the side-shaft. 



THE LAPPEB. 25 





32 Teeth in the wheel on 




the clutch-shaft. 




100 Teeth in the wheel on 




the calender-roller. 




26 Teeth in the wheel on 




the lap-roller. 




3, Draught of the lapper. 


Worked out. 


26 


100 


2600 


32 


5200 




7800 


83200 




32 . 


166400 




249600 


2662400 




42 




5324800 


10649600 


{Continued.) 

2 



26 



COTTON MANUFACTURE. 



C 



D 



B . 



111820800 
9 

1006387200 

4025548800 
3 

13)12076646400 

. 10)923972800 
, 10)92897280 



E 



F 

F 



G 



D 



E 



E 
E 



C 



7)9289728 

4)1327104 

4)331776 

4)82944 



4)20736 



4)5184 



4)1296 



{Continued.) 



. 3)324 
. 3)108 
. 3)36 
. 3)12 



THE LAPPEK. 27 

C 2)4 

D . . . . 2)2 
1 

A. 7 • 7, Diameter of the lap-roller in inches. 

B. 10 X 3 =^ 30 Teeth in the wheel on the lattice- 
roller. 

C. 13 X 3 X 2 78 Teeth in the wheel on the 

feed-roller that takes into the wheel on the undershaft. 

D. 10 X 4 X 2 80 Teeth in the wheel on the 

undershaft that takes into the wheel on the side-shaft. 

E. 4x3x3 36 Teeth in the wheel on the side- 
shaft that takes into the wheel. on the clutch-shaft. 

F. 4x4 = 16 Teeth in the wheel on the clutch- 
shaft that takes into the wheel on the calender-roller. 

Gr. 4x4 = 16 Teeth in the wheel on the calender- 
roller that takes into the wheel on the lap-roller. 

Answer, 

From the particulars found in the preceding example, 
find the draught of the lapper. 

Worked out hy Cancellation. 



1-4 


74 


1-9 


3(04 


1-2-6-42 


78-3 


{Conti 


nued.) 



28 



COTTON MANUFACTURE. 



1-2-32 


8(04-24 


1-2-32 


3644 


1(00 


164 


1-26 


164 



Answer. 



The sa/me without Ccmcellation. 
Dividend, 7 x 30 x Y8 x 80 x 36 x 16 x 16 ^^ ^ 
Divisor, 4 x 9 x 42 x 32 x 32 x 100 x 26 

Answer. 

The lattice-roller and lattice of a lapper are, in effect, 
equal to a roller 4 inches in diameter ; and the lap-roller is 
6.98Y5 inches in diameter. Suppose the lap-roller to be 
the driver of the lattice by- a train of six pairs of wheels ; 
the driving wheels to have respectively 9, 45, 32, 32, 100, 
26, the driven wheels 30, 100, Y2, 32, 15, and 16 teeth. 

What would be the draught of the lapper ? 



Worlced out hy Cancellation. 



14 


6.98Y5-2.68T5 


1-9 


30-34 


14545 


1004 


1-2-32 


Y2-8-24 


1-32 


324 


1400 


154 


1-2.6-26 


164 



2.68T5 



Answer. 



THE LAPPER. 29 



The same without Cancellation. 
• Dividend, 6.98Y5 x 30 x 100 x Y2 x 32 x 15 x 16 _g ^g^g 
Divisor, 4 x 9 x 45 x 32 x 32 x 100 x 26 

Answer. 

The lattice and lattice-roller are, in effect, equal to a 
roller 4 inches in diameter; and the feed-roller is 1^ 
inches in diameter. The lattice-roller has on a wheel 
with 30 teeth, that, by means of an intermediate, takes 
into a wheel with 9 teeth on the feed-roller. 

Required the draught between the lattice and the feed- 
roller. 

WorJced out hj Cancellation. 
1-4 I 1.5-.5 
l-3'9 30-10-2.5 



Answer. 



2.5 X .5 = 1.25 

The same without Cancellation. 

Dividend 30 x 1.5 _ ^ nfc 

Divisor 4x9 

Answer. 

The calender-roller is 4, and the lap-roller 6.9875 inches 
in diameter. The calender-roller has on a wheel with 16 



30 COTTON MAJSrUFACTUEE. 

teeth, that, by means of an intermediate, takes into a wheel 
with 26 teeth on the lap-roller. 

Required the di'aught between the calender-roller and 
the lap-roller. 

Worked out hy Cancellation. 



1-4 
1-6.5-26 



6.98T54.075 
1644 



1.075 

Answer. 



The same without Cancellation. 

Dividend 6.9875 x 16 _ ^^ ^^^ 

Divisor ...... 26 x 4 

Answer. 

The draught between the lattice and the feed-roller is 
1.25, and between the calender-roller and the lap-roller, 
1.075. 

Required the draught between the feed-roller and the 
calender-roller, the total draught being 2.6875. 

Worked out 'by Cancellation. 



14.25 
14.075 



2.6875-2.15-2 



Answer. 



THE LAPPER. 31 



The same without Ccmcellation. 
Dividend 2.6875 



= 2 

Divisor 1.0T5 x 1.25 

Answer. 

From the particulars found in the preceding example, 

find the total draught of the lapper. 

2 X 1.25 X 1.075 = 2.6875 

Answer. 

On the same axis with the lap-roller there is a wheel 
with 26 teeth, that, by means of an intermediate, takes 
into a wheel with 16 teeth on the calender-roller. On 
the calender-roller there is also a wheel with 100 teeth, 
that takes into a wheel with 15 teeth on the clutch-shaft. 
On the clutch-shaft there is a pulley 25,92 inches in dia- 
meter, driven from a pulley on the first driven shaft. On 
the first driven shaft there is a pulley 20 inches in dia- 
meter that drives a pulley 6 inches in diameter on the 
same axis with the first beater. 

What should be the diameter of the pulley on the first 
driven shaft that drives the pulley on the clutch-shaft, to 
drive the lap-roller 5 revolutions per minute, the first 
beater making 1800 in the same time? 



25,92, Diameter of the pul- 
ley on the clutch- 
shaft, in inches. 



32 



COTTON MANUFACTIEBE. 



Teeth in tlie wheel on 
the calender - roller 
that takes into the 
wheel on the lap- 
roller 

Teeth in the wheel on 
the clutch-shaft . . 



16 



15 



Diameter of the pulley 
on the same axis with 
the beater, in inches 6 

Revolutions per minute 
of the first beater, 1800 



26 Teeth in the wheel on 
the lap-roller. 



100 Teeth in the wheel on 
the calender - roller 
that takes into the 
wheel on the clutch- 
shaft. 
20, Diameter of the pulley 
on the first driven 
shaft that drives the 
first beater, in inches. 
5 Revolutions per minute 
of the lap-roller. 



Worked out hy Cancellation. 





25.924.M-.24-.08-.02 


1446 


26 


1-345 


1(00 


1-6 


2044 


148(00 


5 


26 X 5 X .02 : 


2.6 inches. 



Answer. 



THE LAPPER. 33 

The same without Cancellation. 
Dividend, 25.92 x 26 x 100 x 20 x 5 ^ ^ 6 

Answer. 



Divisor, 16 x 15 x 6 x 1800 



From the particulars found in the preceding example, 
find the revolutions per minute of the first beater. 

Worked out hy Cancellation. 
5-1 



1446 

1-345 

1-2.6 

1-6 



26-10 

100 

25.92-8.64:-l.M-.36 

20-5 



100 X 10 X 5 X .36 = 1800 

Answer. 



The same without Ccmcellation. 

Dividend . . 5 x 26 x 100 x 25.92 x 20 _ ^g^^ 

Divisor . . 16 x 15 x 2.6 x 6 

Answer. 

The fan that takes the dust fi-om a lapper is 1 yard in 
diameter, driven from an upright shaft making 180 revo- 
lutions per minute by a train of three pairs of pulleys and 

2* 



34 



COTTON MANUFACTUBE. 



one pair of wheels. The driving wheel has 96 teeth, and 
the respective diameters of the driving pulleys are 40, 30, 
and 20 inches. How many teeth should there be in the 
diiven wheel, and what should be the respective diameters 
of the driven pulleys, to give the circumference of the fan 
a velocity of 1728 yards per minute ? 



Velocity of the circum- 
ference of the fan per 
minute, in yards, 1T28 



180 Revolutions per mi- 
nute of the upright 
shaft. 

96 Teeth in the driving 
wheel. 

40, Diameter of the j&rst 
driving pulley, in 
inches. 

30, Diameter of the sec- 
ond driving pulley, 
in inches. 

20, Diameter of the third 
dri"^dng pulley, in 
inches. 

1, Diameter of the fan, in 
yards. 
3.1416, Circumference. 



THE LAPPEK. 3 


Worked out. 




18045 




96-8 




40 




30 




20 




1 


1-124M4728 


34416-.2618 



15 



120 
40 

4800 
30 

144000 
20 

2880000 
.2618 

23040000 

2880000 

17280000 

5760000 



{Continued.) 



36 



COTTON MAJSTDFACTURE. 



A . . 


4)Y53984.0000 


A . . 


. . 4)188496 


A . . 


. . 4)47124 


D 


. . 2)11T81 


B . . 


. . 2)5890.5 


B . . 


. . 2)2945.25 


B . . 


. 3)1472.625 


B . . 


. . 3)490.875 


D 


. . 7)163.625 



C . 23.375)23.375 



A. 4x4x4 = 64 Teeth in the di'iven wheel. 

B. 3x3x2x2 36, Diameter of the first driven 

pulley, in inches. 

C. 23.375 = 23.375, Diameter of the second driven 
pulley, in inches. 

D. 7x2 . 14, Diameter of the third driven pulley, 
in inches. Answer. 



From the particulars found in the preceding example, 
find the velocity of the circumference of the fan per 
minute. 



THE LAPPEE. 



37 



Worked out hy Cancellation. 





18045-3 


1-8-64: 


96-12 


1-3-36 


40-54 


1-.9354.6T5-23.3T5 


3040-5 


1-2-14: 


20 




1 




34416-3.36-48 



3 X 12 X 5 X 20 X 48 1728 yards. 



Answer. 



The same without Cancellation. 
Dividend, 180 x 96 x 40 x 30 x 20 x 3.1416 ^ 
Divisor, 64 x 36 x 23.375 x 14 



4728 



Answer. 



CAKDING-ENGINE. 

What the Willow and Lapper perform in part, the 
carding-engine completes in a thorough cleansing of the 
cotton. 

The main cylinder of a common-sized carding-engine, 
when carding for medium numbers, makes about 120 
revolutions per minute, and contains 22 sheets of cloth- 
ing, each 30 X 4 inches, containing 400 teeth to the 
square inch, and cards one pound of cotton every 20 
minutes, more or less. Hence every pound of cotton is 



6>i COTTON MANUFACTURE. 

picked from the feed-rollers, fibre by fibre, b}' 120 x 22 

X 30 X 4 X 400 X 20 2534400000 diamond-pointed 

teeth, which by their traction and that of the top cards, 
or slats, untangles the fibres, and lays them more or less 
parallel to each other, and by suitable apparatus, delivers 
them formed into a " sliver." 

The main cylinder of a carding-engine is driven from 
an upright shaft, making 180 revolutions per minute, by 
a train of one pair of wheels and one pair of pulleys. 
The driven wheel has 96 teeth, and the driven pulley is 
12 inches in diameter. How many teeth should there be 
in the driving wheel, and what should be the diameter of 
the driving pulley, to di-ive the main cylinder 120 revolu- 
tions per minute ? 



Revolutions per minute 
of the upright shaft 180 



120 Revolutions per minute 
of the main cylinder. 

96 Teeth . in the di'iven 
wheel. 

12, Diameter of the driven 
pulley, in inches. 



Worked out. 



1-348(0 



12(0-2 

96 

124 



{Cmitinued.) 



CAEDIN.G-ENGINE, 39 

96 

4 

384 
2 

B . . 12)Y68 

A. . . 64)64 

1 

A. 64 ^= 64 Teeth in tlie driving wheel. 

B. 12 ■ 12, Diameter of the driving pulley, in 



inches. 



Answer. 



From the particulars found in the preceding example, 
find the revolutions per minute of the main cylinder. 

Worked out by Ccmcellation. 
180-15 



1-12-96 
142 



64-8 
124 



15 X 8 = 120 

Answer. 

Tfie same without Ccmcellation. 
Dividend .... 180 x 64 x 12 ^ -j^^o 
Divisor .... 96 x 12 

Answer. 



40 



COTTON MANUFACTURE. 



The main cylinder makes 120 revolutions per minute, 
and drives the dothng-cylinder by a train of two pairs of 
wheels. The driven wheels have each 180 teeth. How 
many teeth should there be in each of the driving wheels 
to drive the doffing-cyhnder 9 revolutions per minute ? 



Revolutions per minute 
of the main cylinder, 120 



9 Revolutions per minute 

of the doffing-cylin- 

der. 
180 Teeth in the first driven 

wheel. 
180 Teeth in the second 

driven wheel. 



Worked out. 



142(0 



9 

180-15 

18(0 



18 
15 

90 

18 

2T0 
9 



{^Cooitmued.) 



CARDESTG-KNailSrE. 41 

A 10)2430 



A 3)243 

B 81)81 

1 

A. 10 X 3 = 30 Teeth in the first driving wheel. 

B. 81 ■ 81 Teeth in the second driving wheel. 

Answer. 

From the particulars found in the preceding example, 
find the revolutions per minute of the doffing-cylinder. 



Worked out hy Ccmcellation. 




12(04 


145480 


30-24 


1-948(0 


81-9 



Answer. 



The same without Ccmcellation. 
Dividend . . . . . 120 x 30 x 81 



Divisor 180 x 1-80 

Answer. 



The lap-roller is 4^ inches in diameter, and has on a 



42 



COTTON MANUFACTUEE, 



wheel, that, by means of an intermediate, takes into a 
wheel with 10 teeth on the feed-roller. How many teeth 
should there be in the wheel on the lap-roller, and what 
should be the diameter of the feed-roller to produce a 
draught of 1.1 ? 

4.5, Diameter of the lap- 
roller, in inches. 

10 Teeth in the wheel on 
the feed-roller. 

1.1, Draught. 



Worked out. 



4.5 
10 

45.0 
1.1 

450 
450 

A .... . 3)49.50 

A 11)16.5 

B . . . . 1.5)1.5 
1 



A. 11 X 3=33 Teeth in the wheel on the lap-roller. 



CAKDING-ENGINE. 43 

B. 1.5 = 1.5, Diameter of the feed-roller in inclies. 

Answer. 

From the particulars found in the preceding example, 
find the draught between the lap-roller and the feed- 
roller. 

Worked out l/y Crnicellation. 



1-34.5 
140 



1.54 
33414.1 



1.1 

The sa/me witliout Cancellation. 
Dividend 33 x 1.5 



Divisor 10 x 4.5 



Answer. 

1.1 

Answer. 



The doffing-cylinder is 15, and the drum at the railway 
that drives the belt (belt included) is 10, inches in dia- 
meter. They are connected by a train of four pairs of 
wheels and one pair of pulleys. 

Suppose the drum to be the driver, and the driving 
wheels to have respectively 100.70, 40, and 20 teeth, and 
the driving pulley to be 4 inches in diameter. How 
many teeth should there be in the driven wheels respec- 
tively ; and what should be the diameter of the driven 



44 



COTTON MANTJFACTUEE. 



pulley, to produce a draught of 1.04 between the doffing- 
cylinder and the di-um at the railway ? 

Worked out. 



1(0 



15 

20 

4 

40 

TO 

10(0 

1.04 



1.04 
10 

10.40 

70 

T28.00 
40 

29120 
4 

116480 
20 

2329600 
15 

11648000 
2329600 



34944000 



CAKDING-ENGINE, 45 

E . . 10)34944000 
D . . . 5)3494400 

A 5)698880 

A 2)139776 

A 2)69888 

E . . . 2)34944 
E . . . 2)17472 
E . . . . 2)8736 

B 2)4368 

B 2)2184 

B 2)1092 

B 2)546 

D 3)273 

C 91)91 

1 

A. 5x2x2 , 20 Teeth iu the first driven wheel. 

B. 2x2x2x2 16 Teeth in the second driven 

wheel. 

C. 91 = 91 Teeth in the third driven wheel. 

D. 5x3 15, Diameter of the driven pulley, in 

inches. 



46 



COTTO"N MANUFACTUKE. 



E. 10 X 2 X 2 X 2 
wheel. 



80 Teeth in tlie fourth di-iven 



From the particulars found in the preceding example, 
find the draught between the doffing-cylinder and the 
drum at the railway. 



Diameter of the doffing- 
cylinder, in inches, 15 

Teeth in the fourth driv- 
ing wheel .... 20 

Diameter of the driving 
pulley, in inches . . 4 

Teeth in the third di'iv- 
ing wheel .... 40 

Teeth in the second 
di'iving wheel . . . YO 

Teeth in the first driv- 
ing wheel . . . .100 



10, Diameter of the di'mn, 

in inches. 
80 Teeth in the fourth 

driven wheel. 
15, Diameter of the driven 

pulley, in inches. 
91 Teeth in the third 

driven wheel. 
16 Teeth in the second 

driven wheel. 
20 Teeth in the first di'iv- 

en wheel. 



Worlied out l)y CcmGellaUon. 



1-15 


104 


1-20 


8(0-.2 


1-4 


154 


1-40 


91434.3 


l-Y-70 


164 


140(0 


204 


4 X 1.3 X 


.2 1 .r 



Answer. 



OAEDESra-ENGINE. 47 

The same without Cancellation. 

Dividend, 10 x 80 x 15 x 91 x 16 x 20 _ 
Divisor, 15 x 20 x 4 x 40 x 70 x 100 " ^'^^ 

Answer. 

The feed-roller is driven from the doffing-cylinder by a 
train of two pairs of wheels. The driven wheels have 
respectively 60 and 50 teeth. How many teeth should 
there be in the driving wheels to produce a draught of 80 
between the lap-roller and the railway-head, allowing a 
draught of 1.04 at the railway, and 1.1 between the 
lap-roller and the feed-roller, the feed-roller being 1|-, and 
the doffing-cylinder 15, inches in diameter? 

E".B. — In all cases where the draught of the carding- 
engine is mentioned in this work, the draught at the rail- 
way is included. 

Worked out. 



14.5 



1-8(0 



154(0 

60 

50 

1.1 

1.04-.13 



{Contmued.) 



48 COTTON MANTIFACTURE. 

60 
60 

3000 
1.1 

3000 
3000 

3300.0 
.13 

99000 
33000 

A . . . . 3)429.000 

A 11)143 

B . . . . 13)13 

1 



A. 11x3 33 Teeth in the first driving wheel. 

eheel. 
Answer. 



B. 13 = 13 Teeth in the second driving wheel. 



From the particulars found in the preceding example, 
find the draught of the card. 

Diameter of the feed- I 15, Diameter of the doflfing 

roller, in inches . . 1.5 | - cylinder, in inches. 



CAEDLNG-ENGINE. 



49 



Teeth in the first di*iv- 
ing wheel .... 13 

Teeth in the second 
driving wheel . . .33 



60 Teeth in the first driv- 
en wheel. 
50 Teeth in the second 

di'iven wheel. 
1.1, Draught between the 
lap-roller and feed- 
roller. 
1.04, Draught at the rail- 
way. 



Worked otd hy CoAicellaiion. 



14.5 


1540 


143 


60-2 


1-30-33 


50 




1.14 




1.04-.08 


50 X 10 X 2 


X .08 



80 



Answer. 



The same without Cancellation. 

Dividend . . 15 x 60 x 50 x 1.1 x 1.04 . 
Divisor ... 1.5 x 13 x 33 



Answer. 



The railway-head treated on below has four pairs of 

3 



60 COTTON MANUFACTURE. 

rollers with " Draper's Patent Evener " attached, adapted 
for 12 cards. 

The roller next to the front-roller is called the front- 
in iddle-roller, and the roller next to the back-roller is 
called the back-middle-roller. 

The front-roller is driven from the back-roller by a 
train of three pairs of wheels, and one pair of cones. 
The back-middle-roller and the front-middle-roller are 
each driven from the back-roller by an intermediate 
wheel. 

The tube throngh which the sliver passes, and the 
apparatus for moving the belt on the cones, are so adjust- 
ed, that, if the fleece delivered from one of the cards 
should break, they will cause the belt to move from the 
large end of the driving cone sufficient to reduce the 
speed of the front-roller -^ ; and, if the fleece should break 
from two cards, j^^, etc., etc., — thus keeping the sliver 
delivered of a uniform size. 



EAILWAT-HEAD. 

The front-roller is 1^ inches in diameter, and has on 
a wheel, that, by means of an intermediate, takes into a 
wheel with 80 teeth on the same axis with the delivering 
balls. How many teeth should there be in the wheel on 
the front-roller, and what should be the diameter of the 
delivering balls, to produce a draught of 1.02 ? 




draper's railway head. 



BAILWAT-HEAD. 



51 



Worked out. 
1.02 
1.25 

80 



B . 



1.25 

80 



100.00 
1.02 

20000 
100000 

. 3)102.0000 

. . . 34)34 

1 



A. 
B. 



34 
3 = 



= 34 Teeth in the wheel on the front-roller. 
3, Diameter of the delivering balls, in inches. 

Answer. 



The front-roller is IJ, and the delivering balls 3, inches 
in diameter. The front-roller has on a wheel with 34 
teeth, that, by means of an intermediate, takes into a 
wheel with 80 teeth, on the same axis with the delivering 
balls. Beqtdred the draught. 



52 COTTON MANUFACTUKE. 



Diameter of the front- 
roller, in inches, 1.25 

Teeth in the wheel on 
the same axis with 
the delivering balls, 80 



3, Diameter of the deliver- 
ing balls, in inches. 

34 Teeth in the wheel on 
the front-roller. 



Worlied out lyy Ccmcellation. 



14.25 

1-80 



3-2.4-.03 
34 



Answer. 



34 X .03 = 1.02 

The same loithout Cancellation. 
Dividend ..... 3 x 34 



= 1.02 
Divisor ...... 1.25 x 80 

Answer. 



The front-roller is driven from the back-roller by a 
train of 3 pairs of wheels, and one pair of cones. The 
driven wheels have respectively 100, 18, and 51 teeth ; 
and the driven cone is 3 inches in diameter at the small 
end. 

How many teeth should there be in the driving wheels 
respectively, and what should be the diameter of the large 
end of the driving cone, to produce a draught of 2 at the 
railway-head, allowing a draught of 1.02 between the 



RAILWAY-HEAD. 



53 



front-roller and the delivering balls, the front-roller being 
1^, and the back-roller, 1 inch in diameter ? 

N.B, — The belt is always at the large end of the driv- 
ing cone, and, of course, at the small end of the driven 
cone, when the cards are utihziiig their maximum quan- 
tity. 

Worked out. 



1-1.02 
14.25 



2 

1 

100 

18 

3 

51-5040 



10 
3 



120 

18 

960 
120 

2160 
100 

216000 
2 



432000 



54 



COTTON MANUFACTURE, 


A . 




10)432000 


B 




. 5)43200 


B 




. 5)8640 


A . 




. 2)1728 


A . 




. . . 2)864 


A . 




. . . 2)432 




D. 


. . . 2)216 




D. 


. . . 2)108 




D. 


. . . 2)54 




D. 


. . . 2)2Y 


B 


• • 


. . 3)13.5 


C 


1 

1 • • 


. 4.5)4.5 
1 



A. 10 X 2 X 2 X 2 80 Teeth in the first driving 

wheel. 

B. 5x5x3 == T5 Teeth in the second di-iving 
wheel. 

C. 4.5 4^, Diameter of the large end of the di-iv- 

ing cone, in inches. 

D. 2x2x2x2 16 Teeth in the third di-iving 

wheel Answer. 



KAIL WAY-HEAD. 



55 



From the particulars found in the preceding example, 
find the total draught at the railway-head. 



Diameter of the back- 
roller, in inches . . 1 

Teeth in the first driven 
wheel 100 

Teeth in the second 
driven wheel ... 18 

Diameter of the small 
end of the driven 
cone, in inches . . 3 

Teeth in the third driv- 
en wheel .... 51 



1.02, Draught between the 
front-roller and de- 
livering balls. 
1.25, Diameter of the front- 
roller, in inches. 
80 Teeth in the first driv- 
ing wheel. 
T5 Teeth in the second 
driving wheel. 
4.5, Diameter of the large 
end of the driving 
cone, in inches. 
16 Teetli in the third 
driving wheel. 



Worked out hy Ca/ncellation. 




1.02-.02 


1 


1.25 


1-5400 


8044 


1448 


Y545-5 


1-3 


4.54 


1-51 


16 



16 X 5 X 1.25 X .02 



Answer. 



56 



COTTON MANUFACTDEE. 



The same witJiout Ccmcellation. 

Dividend, 1.02 x 1.25 x 80 x Y5 x 4.5 x 16 ^ ^ 

Divisor, 100 x 18 x 3 x 51 

Answer. 

From the particulars given to find tlie di'aught be- 
tween the back-roller and the front-roller, and the parti- 
culars given to find the draught between the front-roller 
and the delivering balls, find the total draught. 

Worked out hy CcmcellaUon, 

34 

34-1 

1.25-1 

804 

Y5-.75-.5 
4.54 
164 



14.25 


1-80 


1 


1400 


1448 


1-3 


4.5-51 



4 X .5 



Answer. 



The same without Cancellation. 
Dividend, 3 x 34 x 1.25 x 80 x Y5 x 4.5 x 16 ^ ^ 



Divisor, 



1.25 X 80 X 100 X 18 x 3 X 51 



Answer. 



EAILWAT-HEAD. 57 

From tlie particulars found in the preceding example, 
find tlie draught between the back and the front rollers. 

Worked out hy Cancellation. 



1 


1.25 


1-5400 


8044 


1448 


Y5-25-5 


1-3 


4.54 


1-51 


16-.3A 


1.25 X 5 X .3 


^ 1.96A 



Answer. 



The same wiiliout Cancellation. 



Dividend, 1.25 x 80 x 75 x 4.5 x 16 ^-^^^^ 

Divisor, 100 x 18 x 3 x 51 ' ^^ 

Answer. 



The back and the back-middle rollers are each 1 inch in 
diameter. The back-roller has on a w^heel with 21 teeth. 
How many teeth should there be in the wheel on the back- 
middle-roller to produce a draught of 1.05 ? 

WorTced out hy Cancellation. 
14.05 I 21-20 

20 

Answer. 



68 COTTON MANUFACTUKE. 

From the particulars found in the preceding example, 
id the drai 
middle-roller. 



find the draught between the back-roller and the back- 



Worked out h/ Ca/ncellation. 
1-20 I 21-1.05 



1.05 

Answer. 



The back-roller and the front-middle-rollers are each 1 
inch in diameter. The front-middle-roller has on a wheel 
with 20 teeth. How many teeth should there be in the 
wheel on the back-roller to produce a draught of 1.25 ? 

20 X 1.25 = 25 

Answer. 

From the particulars found in the preceding example, 
find the draught between the back-roller and the front- 
middle-roller. 

Wm^hed out hy Cancellation. 
1-20 I 25-1.25 

1.25 

Answer. 

From the wheels given to find the draught between the 



BAILWAT-HEAD. 59 

back-roller and the back-middle-roUer ; and the wheels 
given to find the draught between the back-roller and 
the front-middle-roller, find the draught between the 
back-middle-roUer and the front-middle-roller. 



Worked out hy Ca/iicellation. 
1-20 I 254. 
1-21 204 



1-20 I 254.19^'j- 



'sT 



Answer. 



The same without Cancellation. 

Dividend 25 x 20 _.. ..q , 

Divisor 21 x 20 

Answer. 

From the particulars given to find the total draught, 
and the particulars given to find the draught between 
the front-roller and the back-roller, find the draught 
between the front-roller and the delivering balls. 



Worked out hy Cancellation. 




1.02 


1 


1.254 


1400 


804 


148 


754 


1-3 


4.54 


{Conti 


nued.) 



60 



COTTON MANUFACTUEE. 



1-51 
1-1.25 

1-80 

1-75 

14.5 

146 



164 

1 

1004 

184 

34 

514 



1.02 



Answer. 



The same without Ccmcellation. 

1.02 X 1.25 X 80 X Y5 X 4.5 X 16 X 100 X 18 X 3 X 51 

100 X 18 X 3 X 51 X 1.25 x 80 x Y5 x 4.5 x 16 

= 1,02 Answer. 



K.B. — The above result will be obtained by dividing 
the total draught by t]ie draught between the back-roller 
and the front-roller. See the following example. 

The draught between the back and front rollers is 
1.96^, and the total draught is 2, Eequired the draught 
between the delivering balls and the front-roller. 

Worked out hy Cancellation. 
l^.B.— 1.96A 



'TT 



1 00 



1400 



2 
51-.51 



2 X .51 



1.02 



Answer. 



KAIL WAT-HEAD. 



61 



The same without Ca/ncellation 
Dividend 51 x 2 



Divisor 



100 



=1.02 
Answer. 



From the particulars given to find tlie total draught, 
the draught between the front-roller and the delivering 
balls, and the draught between the back-roller and the 
front-middle-roUer, find the draught between the front- 
middle-roller and the front-roller. 



WorTced out ly Cancellation. 



1-1.25 

1-80 

1 

1(00 

1448 

1-3 

1-51 

1-3 

1-34 

1-25 



34 

344 

1.254 

804 

Y5-34 

4.54 

164 

1.25 

8(0-A 
2(0 



4 X 1.25 X 2 x^ 



1.56M 



Answer. 



G2 COTTON MA2JUFACTUEE. 

The smne without Cancellation. 

3 X 34 X 1.25 X 80 X 75 X 4.5 x 16 x 1.25 x 80 x 20 
1.25 X 80 X 100 X 18 X 3 X 51 X 3 X 34 X 25 

=1 .56ff Answer. 

The draught between the delivering balls and the front- 
roller is 1.02, and the draught between the back-roller 
and the front-middle-roller is 1.25. Required the draught 
between the front-middle-roller and the front-roller, the 
total draught being 2. 

Worked out hy Cancellation. 

24.64.56tt 
14.02 
14.25 



Answer. 



1.56ii 

The sa/me without Cancellation. 

Dividend .... 2 _-, 

Divisor 1.25 x 1.02 ~ ' 

Answer. 

The draught between the back-middle-roller and the 
back-roller is 1.05. The di*aught between the back- 
middle and the front-middle-roller 1.19^\. The draught 



EAILWAT-HEAD. 63 

between the front-middle-roUer and the front-roller is 
1.56ff. The draught between the front-roller and the 
delivering balls is 1.02. 
Eequired the total draught. 

Iir.B.-1.19^V = ff 



1.56M 



80 



Worked out hy Cancellation. 
1.05-.05 



1-21 
1-51 



25 
80 
1.02-.02 



80 X 25 X .05 X .02 = 2 



Answer. 



The sa/me without Cancellation. 
Dividend . . . 1.05 x 25 x 80 x 1.02 



=2 



Divisor .... 51 X 21 . 

Answer. 

The can that receives the sliver stands upon and 
revolves with the disc, and, in practice, it is found that 
the velocity of its circumference should be to that of the 
delivering balls as 1 to 8. 

The delivering balls are 3 inches in diameter, and drive 
the disc by a train of 2 pairs of wheels. The driven 



04: 



COTTON MA.NUFACTUKE. 



.wheels have respectively 24: and 180 teeth. How many- 
teeth should there be in the driving wheels respectively, 
and what should be the diameter of the can, to give its 
circumference a velocity ^ of that of the delivering balls ? 



Worked out. 


1-8 


1 




3 




24-3 




180 


180 


3 


510 


3 


B . . . . 2)1620 


C . . . ■ . 2)810 


C. . . . 3)405 


C. . . . 3)135 


B 3)15 


A 3)15 


A ...... 5)5 




1 



KAIL WAY-HEAD. 



65 



A. 5x3 = 15 Teeth in the first driving wheel. 

B. 3x2 . 6 Teeth in the second driving wheel. 

C. 3x3x2 . 18, Diameter of the can, in inches. 

Answer. 

From the particulars found in the preceding example, 
find the ratio of velocity of the circumference of the 
delivering balls to that of the can, supposing that of the 
can to be 1 : 



Diameter of the can, in 
inches 18 

Teeth in the first driv- 
ing wheel .... 15 

Teeth in the second 



1 Eatio of velocity of the 
circumference of the 
can. 
3, Diameter of the deliv- 
ering balls, in inches. 
24 Teeth in the first driv- 
en wheel. 
180 Teeth in the second 



driving wheel ... 6 


driven wheel or disc. 


Worked out hi 

148 
1-345 

1-2-6 


/ Cam^Gellation. 

1 
3-1 

24-8 
180-10-5-1 



Answer. 



GQ COTTON MANUTAOTUEE. 

The same without Ccmcellation. 
Dividend 3 x 24 x 180 



= 8 



Divisor 18 x 15 x 6 

Answer. 



DBAWING-FBAME. 

As has been shown, the object attained by the previous 
processes in the carding department is a thorough cleans- 
ing of the cotton, untangling its fibres, laying them more 
or less parallel with each other, and forming them into a 
sliver. 

The object to be attained at the drawing-frame is to 
repeatedly double and draw the slivers until they mutually 
correct any unevenness that may have occurred in their 
formation, and lay the fibres perfectly parallel with each 
other and the sliver. 

The front-roller at the drawing frame is 1^, and the 
delivering balls 3 inches in diameter. The front-roller 
has on a wheel with 27 teeth, that, by means of an inter- 
mediate, takes into the wheel on the same axis with the 
delivering balls. How many teeth should there be in the 
wheel on the same axis with the delivering balls to pro- 
duce a draught of 1.08 ? 



Diameter of the front- 
roller, in inches . .1.25 



3, Diameter of the deliv- 
ering balls, in inches. 



DEAWING-FBAME. 67 



27 Teeth in the wheel on 
the front-roller. 



Draught .... .1.08 



Worked out hy Crnicellation. 
14.25 3 

27-21.6-20 
14.08 



20 X 3 60 

Answer. 



Tlie sa/me without Ccmcellation. 
Dividend 27 x 3 



=60 



Divisor 1.08 x 1.25 

Answer. 



From the particulars found in the preceding example, 
find the draught between the front-roller and the deliver- 
ing balls. 

Worked out hy Cancellation. 



14.25 
1-20-60 



34 

27-21.64.08 



1.08 

Answer. 

The same without Cam^cellation. 

Dividend ..... 27 x 3 ^ -; ^^ 

Divisor 60 x 1.25 

Answer. 



68 



COTTON MANUFACTURE. 



The front-roller is 1-|, and tlie back-roller is 1 inch in 
diameter. The fr-ont-roUer wheel has 27 and the change 
wheel 36 teeth. How many teeth should there be in the 
top-carrier and the back-roller wheel to produce a draught 
of 4 at the di-awing head, the draught between the front- 
roller and the delivering balls being 1.08 ? 



Diameter of the front- 
roller, in inches . . 1.25 



Draught between the 
front-roller and the 
deliverino; balls . .1.08 



1, Diameter of the back- 
roller, in inches. 
2Y Teeth in the wheel on 

the front-roller. 
36 Teeth in the change 
wheel. 
4z, Total draught. 



Worhed out. 


14.25 


1 




2r-25-20 




36 


14.08 


4 



36 

20 



T20 



(Continued.) 





DKAWmG-FR.AME, 




Y20 
4 


B 


. . . 10)2880 


A . 


.... 4)288 
.... T2)Y2 



69 



A. T2 Y2 Teeth in the top-carrier. 

B. 10 X 4: = 40 Teeth in the back-roller wheel. 

Answer. 

From the particulars found in the preceding example, 
find the total draught at the drawing head. 

Worked out hy Cancellation. 



1 
1-36 
1'2T 



1.25 
40 

72-2 
1.08-.04 



40 X 2 X 1.25 X .04 = 4 

The same without Ca/ncellation. 
Dividend . . 1.25 x40 x Y2 x 1.08 



Answer. 



4 



Divisor ... 36 x 2Y 

Answer. 



70 



COTTON MANUFACTURE. 



BOBBIN AND FLY-FKAME, 

An upright shaft makes 180 revolutions per minute, 
and has on a wheel that takes into a wheel with 96 teeth 
on a lying shaft. On the lying shaft there is a pulley 
that drives a pulley 16 inches in diameter on a counter- 
shaft. On the countershaft there is a pulley that di'ives a 
pulley 10 inches in diameter on the first driven shaft of 
the fly-frame. How many teeth should there be in the 
wheel on the upright shaft, and what should be the 
diameter of the driving pulleys on the lying and the 
countershafts to drive the first driven shaft 288 revolu- 
tions per minute? 



Revolutions per minute 
of the upright shaft, 180 



288 Revolutions per minute 
of the first driven 
shaft. 

96 Teeth in the wheel on 
the lying shaft. 

16, Diameter of the driven 
pulley on the coun- 
tershaft, in inches.. 

10, Diameter of the pulley 
on the first driven 
shaft of the fly-frame, 
in inches. 



BOBBm AND FLY-FRAME. 



71 



Worked out. 


l-348(0 


288-96 
9646 




16 




1(0 


96 


16 


676 


96 


1536 


16 


9216 


A . . . 


1536 


. 8)24576 


B . . . 6)3072 


A ..... 8)512 
B .... 4)64 


C . . . . 16)16 
1 


A. 8 X 8 : 64 Teeth 

shaft. 


in the wheel on the nprigh 



72 COTTON MANUFACTUKE. 

B. 6x4 == 24, Diameter of tlie di-iving pulley on 
the lying shaft, in inches. 

C. 16 == 16, Diameter of the diiving pulley on the 
countershaft, in inches. 

Answer. 

From the particulars found in the preceding example, 
find the revolutions per minute of the first driven shaft of 
the fly-frame. 



Worked out hy Cancellation. 




18(0 


1-8-96 


64-8 


146 


24-2 


1(0 


164 


18 X 8 X 


2 288 



Answer. 



The same witJiout Cancellation 
Dividend . . . 180 x 64 x 24 x 16 



=288 



Divisor ... 96 x 16 x 10 

Answer. 



The first driven shaft of the fly-frame makes 288 revo- 
lutions per minute, and has on a wheel that takes into a 
wheel with 42 teeth on the sj)indle-shaft. On the spindle- 
sliaft there is a wheel that takes into a wheel with 24 



BOBBIN AND FLY-FKAME. 



Y3 



teeth on the spindle. How many teeth should there 
be in the wheel on the first driven shaft, and the driving 
wheel on the spindle-shaft, to drive the spindles 720 
revolutions per minute? 



Revolutions per minute 
of the first driven 
shaft of the fly-frame, 288 



720 Revolutions per minute 

of the spindles. 
42 Teeth in the diiven 

wheel on the spindle 

shaft. 
24 Teeth in the wheel on 

the spindle. 



Worked out. 



1-24-288 



720-60 

42 

24-1 



42 
60 

A 10)2520 

A 7)252 

B 36)36 

1 

A. 10 X 7 = 70 Teeth in the wheel on the first 

driven shaft of the fly-frame. 

4 



74 



B. 36 



spindle shaft. 



COTTON MANUFACTURE. 

36 Teeth in the di'iving wheel on the 

Answer. 



The first driven shaft makes 288 revolutions per minute, 
and has on a wheel with TO teeth that takes into a wheel 
with 42 teeth on the spindle-shaft. On the spindle-shaft 
there is also a wheel with 36 teeth that takes into a wheel 
with 24 teeth on the sphidle. How many revolutions 
per minute does the spindle make ? 



Teeth in the driven 
wheel on the spindle- 
shaft ...... 42 

Teeth in the wheel on 
the spindle .... 24 



288 Revolutions per minute 
of the first driven 
shaft. 

70 Teeth in the wheel on 
the first driven shaft. 

36 Teeth in the driving 
wheel on the spindle- 
shaft. 



WorTced out hy Cancellation. 

288-48 



1-642 
1-2-24 

48 X 5 X 3 



7040-5 
36-3 



T20 



Answer. 



BOBBIN XSD FLY-FRAME. TO 

The same without Cancellation. 

Dividend . . . 288 x YO x 36 _ ^^q 
Divisor .... 42 X 24 

Answer. 

In treating on the epicyclic train of wheels, or what is 
technically called the differential coupling, it has been 
thought best to name each wheel and its use. The object 
to be obtained by the differential coupling is gradually to 
increase the speed of the bobbin at the same rate as its 
diameter increases, since it is essential that the bobbin 
and the front-roller have equal surface velocities. 

The train of wheels in the differential coupling are 5 
in number, 3 of which are on the same axis with the first 
driven shaft. The first wheel is made fast to the first 
driven shaft, and is called the fast internal wheel. The 
second or middle wheel revolves loose upon the first 
driven shaft, and is called the differential wheel. The 
third wheel is made fast to a hollow cylinder that 
revolves loose upon the first driven shaft, and is called 
the loose internal wheel. The other two (only one of 
which is necessary) are intermediate or carrying wheels, 
connecting the fast and loose internal wheels : they are 
fast to, and have their axis in the plane of the differen- 
tial wheel. The fast and loose internal wheels are both 
of the same dimensions, and need not be taken into ac- 



70 COTTON MAJSrUFACTUKK. 

count ; but there is a wheel outside of the difibrential 
coupling, called the external wheel, that is made fast to 
the same hollow cylinder as the loose internal wlieel, 
which, with the differential wheel, will be fomid in the 
following examples, and will answer every purpose for 
calculating anything pertaining to the differential coup- 
ling. 

It is obvious that if the differential wlieel were lield 
fast, the external wlieel and the fast and loose internal 
wheels would all revolve at the same speed, and that, if it 
were made to revolve at the same speed as the fast inter- 
nal wheel, the external wheel would stand still. Hence 
it is by having the differential wheel revolve in the same 
direction as the fast internal wheel, but at a slower rate, 
equal to the difference in speed between the flyer and the 
bobbin, that the surface velocity of the bobbin is made to 
keep pace with that of the front-roller. 

!N.B. — In the following example, the differential wheel 
is supposed to stand still. 

The external wheel makes 288 revolutions per minute, 
and takes into a wheel with 42 teeth on the bobbin-shaft. 
On tlie bobbin-shaft there is a wheel that takes into a 
wheel with 40 teeth, to which tlie bobbin is made fast. 
How many teeth should there be in the external wheel, 



BOBBnsr AND FLY-FEAME. 



YT 



and the driving wheel on the bobbin-shaft, to drive the 
bobbin 720 revohitions per minute? 



Revolutions per minute 
of the external wheel, 288 



T20 Revolutions per minute 
of the bobbin. 

42 Teeth in the driven 
wheel on the bobbin- 
shaft. 

40 Teeth in the wheel to 
which the bobbin is 
made fast. 



Worked out. 



1-2-24-288 



720-60-5 

42-21 

40 



21 
5 

105 
40 

A 10)4200 

A. . . . . 10)420 

B 42)42 

1 



78 



COTTON MANUFACTURE. 



A. 10 X 10 100 Teeth in tlie external wheel. 

B. 42 ■ 42 Teeth in the driving wheel on the hob- 
bin-shaft. Answer. 

N.B. — In the following example the differential wheel 

is supposed to stand still. 

The external wheel makes 288 revolutions per minute, 
has 100 teeth, and takes into a wheel with 42 teeth on 
the bobbin-shaft. On the bobbin-shaft there is also a 
wheel with 42 teeth that takes into a wheel with 40 teeth, 
to which the bobbin is made fast. How many revolutions 
per minute does the bobbin make ? 

288 devolutions per minute 
of the external wheel. 

100 Teeth in the external 
wheel. 



Teeth in the driven 
wheel on the bobbin- 
shaft 42 

Teeth in the wheel to 
which the bobbin is 
made fast .... 40 



42 Teeth in the driving 
wheel on the bobbin- 
shaft. 



Woi'Tced out hy Cancellation. 

288-Y2 



1-42 
1-4(0 



10(0 
424 



T2 X 10 



T20 



Answer. 



BOBBIN AND FLT-FEAME. 



79 



The same without Cancellation. 
Dividend . . . 288 x 100 x 42 



Divisor . 



42 X 40 



:720 

Answer. 



The first driven shaft makes 288 revolutions per minute, 
and has on a wheel with 20 teeth, that takes into a wheel 
on the grooved shaft. On the other end of the grooved 
shaft there is a wheel with 100 teeth, that takes into a 
wheel on the front-roller. How many teeth should there 
be in the wheel on the grooved shaft, that takes into the 
wheel on the first driven shaft, and the wheel on the 
front-roller, to drive the front-roller 96 revolutions per 
minute ? 



Kevolutions per minute 
of the front-roller . . 96 



288 Revolutions per minute 

of the first driven 

shaft. 

20 Teeth in the wheel on 

the first driven shaft. 

100 Teeth in the wheel 
that takes into the 
wheel on the front- 
roller. 



80 



COTTON MANUFACTURE. 



Worked out. 



1-8-96 



288-24-3 

20 

100 



A 
A 



20 
3 

60 
100 

10)6000 



.... 10)600 

B 60)60 

1 

A. 10 X 10 100 Teetli in tlie wheel on tlie front- 
roller. 

B. 60 60 Teeth in the driven wheel on the 
grooved shaft. Answer. 

The first driven shaft makes 288 revolutions per minute, 
and has on a wheel with 20 teeth that takes into a wheel 
with 60 teeth on the grooved shaft. On the other end of 
the grooved shaft there is a wheel with 100 teeth, that 
takes into a wheel with 100 teeth on the front-roller. 
How many revolutions per minute does the fr*ont-roUer 
make? 



BOBBIN AND FLY-FBAME. 



81 



Teeth in the driven 
wheel on the grooved 
shaft 60 

Teeth in the wheel on 
the front-roller . . 100 



288 Revolutions per minute 

of the lii'st di'iven 

shaft. 
20 Teeth in the wheel on 

the first drive!i shaft. 
100 Teeth in the driving 

wheel on the grooved 

shaft. 



Worked out l)y GcmcellaUon. 

28848 
1-6(0 2(0 
1400 1004 



48x2. 



96 



Answer. 

TJie sa/me without Ccmcellation. 

Dividend .... 288 x20 xlOO _ q^ 

Divisor 100x60 

Answer. 



The front-roller is 1^ inches in diameter, and makes 96 
revolutions per minute, and the spindle makes Y20 revolu- 
tions per minute. How many turns of twist per inch is 
there in the roving ? 



82 



COTTON MAJfUFACTUKE. 



Revolutions per minute 


Y20 Revolutions per minute 


of the front-roller . . 96 


of the spindle. 


Diameter of the front- 




roller, in inches . .1.25 




Ratio of circumference 




to diameter . . . 3.1416 




Worked out hy Cancellation,. 


1-8-96 


'r20-60-7.5-6-1.9 


1-1.25 




1-3.1416 





1.9 

The same without Cancellation. 
Dividend .... 720 



Answer. 



1.9 



Divisor 96 x 1.25 x 3.1416 



Answer. 

The spindle makes 720 and the front-roller 96 revolu- 
tions per minute. How many revolutions does the spindle 
make while the front-roller makes 1 ? 

Worked out hy Cam^cellation. 
1-8-96 I 720-60-7.5 



7.5 



Answer. 



BOBBIN AND FLY-FRAME. 83 

N.B. — If it is admitted that the diameter of the empty 
bobbin is equal to that of the front-roller, the spindle 
making T|-, while the front-roller makes 1 revolution, it 
will be evident that the bobbin will have to make 1 revo- 
lution less than the spindle in the same time, in order to 
wind on the roving as fast as it is delivered by the front- 
roller (making no allowance for shrinkage in twisting), 
until the first layer is wound on to the bobbin; there- 
fore the bobbin will make 6|, while the spindle makes 7^ 
revolutions. 

If the bobbin makes 6^, while the spindle makes Y^ 
revolutions, how many revolutions per minute will the 
bobbin make, if the spindle makes 720 ? 

Worked out hy Ccmcell^ition. 
720-2400 



1-.34.5-7.5 



6.54.3-.26 



2400 X. 26 = 624 

The same without Ccmeellation. 
Dividend 720x6.5 



Answer. 



624 



Divisor 7.5 

Answer. 

The bobbin makes 624 revolutions per minute, while 
winding on the first layer of roving. The wheel to which 



84 



COTTON MANUFACTUKE. 



the bobbin is made fast has 40 teeth, and takes into a 
wheel with 42 teeth on the bobbin-shaft. On the bobbin- 
shaft there is also a wheel with 42 teeth that takes into 
the external wheel, which has 100 teeth. How many 
revolutions per minute does the external wheel make ? 

624 Revolutions per minute 
of the bobbin. 
40 Teeth in the wheel to 



Teeth in the wheel 
on the bobbin-shaft 
that takes into the 
wheel to which the 
bobbin is made fast, 42 

Teeth in the external 
wheel 100 



42 



which the bobbin is 
made fast. 



Teeth in the wheel 
on the bobbin-shaft 
that takes into the 
external wheel. 



Worked out hy CcmcellaUon. 
624 



142 

140(0 



4(0-.4 
424 > 



624 X. 4: 



249.6 



Answer. 



The 80/nie without Cancellation. 

Dividend 624 x 40 x 4 2 

Divisor 100x42 



= 249.6 



Answer. 



BOBBIN AND FLY-FRAME. 85 

The first driven shaft makes 288, and the external 
wheel 249.6 revolutions per minute, while winding the 
first layer of roving on to the bobbin. How many revo- 
lutions per minute has the external wheel been retarded, 
admitting that it would have revolved at the same speed 
as the first driven shaft, if the differential wheel had stood 
stiU? 

288.0 
249.6 



38.4 Answer. 

The wheel to which the bobbin is made fast has 40 
teeth, and takes into a wheel with 42 teeth on the bobbin- 
shaft. On the bobbin-shaft there is also a wlieel with 42 
teeth that takes into the external wheel, which has 100 
teeth. The differential wheel retards the external wheel 
38.4 revolutions per minute. How many revolutions per 
minute is the bobbin retarded ? 

38.4 Revolutions per minute 
that the external 
wheel is retarded. 
Teeth in the wheel on 100 Teeth in the external 

the bobbin-shaft that wheel, 

takes into the exter- 
nal wheel .... 42 

{Continued.) 



86 



COTTON MANUFACTURE. 



Teeth in the wheel to 
which the bobbin-shaft 
is made fast ... 40 



42 Teeth in the wheel on 
the bobbin-shaft that 
takes into the wheel 
to which the bobbin 
is made fast. 



Worked out hy Cancellation. 




38.4 


142 


10(0-2.5 


14(0 


424 


38.4 X 2. 


5 96 



The same without Cancellation. 
Dividend . ... 38.4 x 100 x 42 
Divisor 42 x 40 



Answer. 



= 96 



Answer. 



K.B. — It will be observed from the above that the bob- 
bin, while winding on the first layer of roving, is retarded 
exactly the same number of revolutions per minute as the 
front-roller makes, which is right (making no allowance 
for shrinkage in twisting), because the empty bobbin and 
the front-roller are both of the same dimensions, and the 
winding on is effected by the bobbin falling behind the 
spindle. 



BOBBEST AND FLT-FKAME. 



87 



The first driven shaft makes 288 revolutions per minute, 
and has on a wheel with 20 teeth that takes into a wheel 
with 60 teeth on the grooved shaft. On the grooved 
shaft there is a pulley 5 inches in diameter that drives tlie 
cone at the small end. 

On the same axis with the cone there is a wheel with 54 
teeth that takes into a wheel on a short shaft. On the other 
end of the short shaft there is a wheel with 32 teeth that 
takes into the differential wheel. How many teeth should 
there be in the driven wheel on the short shaft and the 
differential wheel, and what should be the diameter of 
the small end of the cone, to drive the differential wheel 
38.4: revolutions per minute ? 

l^.B. — The belt is always at the small end of the cone 
at the commencement of the bobbin, when the winding 
on is effected by the bobbin falling behind the spindle ; 
and every time the differential wheel makes one revolu- 
tion, it reduces that of the external wheel the same. 



Revolutions per minute 
of the differential 
wheel 38.4 

Teeth in the wheel on 
the grooved shaft . 60 



288 Revolutions per minute 
of the first di'iven 
shaft. 
20 Teeth in the wheel on 
the first driven shaft. 
5 Diameter of the pulley 
on the grooved shaft, 
in inches. 



88 



COTTON MANUFACTURE. 



54 Teetli in the wheel on 
the same axis with 
the cone. 

32 Teeth in the wlieel that 
takes into the differ- 
ential wheel. 



1-3.2-38.4 


288-24-8 


1-3-60 


204 




5 




54 




3240 


54 
10 


540 
5 


2700 
8 


. . . 10)21600 


B. . . . 10)2160 


A .... 2)216 


C . . 

B. . . 

{ConUnued.) 


. . 2)108 
. . 2)54 



BOBBm AJSTD FLT-FEAME, 89 

B 3)27 

C 3)9 

C 3)3 

1 



A. 2 ^= 2 Diameter of the small end of the cone, in 
inches. 

B. 10 X 2 X 3 :^= 60 Teeth in the driven wheel on 
the short shaft. 

C. 10 X 2 X 3 X 3 180 Teeth in the differential 

wheel. 

Answer. 



The first driven shaft makes 288 revolutions per minute, 
and has on a wheel' with 20 teeth that takes into a wheel 
with 60 teeth, on the grooved shaft. On the grooved 
shaft there is a pulley 5 inches in diameter, that drives 
the cone at the small end, which is 2 inches in diameter. 
On the same axis with the cone there is a wheel with 54 
teeth that takes into a wheel with 60 teeth, on a short 
shaft. On the other end of the short shaft there is a 
wheel with 32 teeth, that takes into the differential wheel, 
which has 180 teeth. How many revolutions per minute 
does the differential wheel make ? 



90 



COTTON M^ySTUFACTURE. 



Teeth in tlie wheel on 
the grooved shaft . 60 



Diameter of the small 
end of the cone, in 
inches 2 

Teeth in the di*iven 
wheel, on the short 
shaft 60 

Teeth in the differen- 
tial wheel . . . .180 



288 Revolutions per minute 

of the first driven 

shaft. 

20 Teeth in the wheel, on 

the first driven shaft. 

5 Diameter of the pulley 
on the grooved shaft, 
in inches. 

54 Teeth in the wheel on 
the same axis with 
the cone. 

32 Teeth in the wheel that 
takes into the differ- 
ential wheel. 



Worked out hy Cmicellation. 



1-3-60 

1-2 

1-5-60 

1-5-20480 



288-24-84-1 

204 

54 

54-6 

32-6.4 



6.4 X 6 



38.4 



The same without Cancellation. 
Dividend . . 288 x 20 x 5 x 54 x 32 
Divisor . . . 



Answer. 



= 38.4 



60 X 2 X 60 X 180 



Answer. 



BOBBESr AJSTD FLY-FKAME. 



91 



The first driven shaft makes 288 revolutions per minute, 
and has on a wheel with 20 teeth that takes into a wheel 
with 60 teeth, on the grooved shaft. On the grooved 
shaft there is a pulley 5 inches in diameter that drives the 
cone at the small end, which is 2 inches in diameter. On 
the same axis with the cone there is a wheel with 54 
teeth, that takes into a wheel with 60 teeth, on a short 
shaft. On the other end of the short shaft there is a 
wheel with 32 teeth, that takes into the diiferential wheel, 
which has 180 teeth. The external wheel has 100 teeth 
and takes into a wheel with 42 teeth, on the bobbin shaft. 
On the bobbin shaft there is also a wheel with 42 teeth, 
that takes into a wheel with 40 teeth, to which the bobbin 
is made fast. How many revolutions per minute is the 
bobbin retarded ? 



]Sr.B. — The above includes the whole train of wheels, 
pulley, and cone leading from the first driven shaft 
through the differential coupling to the bobbin. 

288 Revolutions per minute 

of the first di'iven 

shaft. 

Teeth in the wheel, on 20 Teeth in the wheel, on 

the grooved shaft . 60 the first driven shaft. 

Diameter of the small 5 Diameter of the pulley 

end of the cone, in on the grooved shaft, 

inches 2 in inches. 



92 



COTTON MANUFACTUEE. 



Teeth in the driven 
wheel, on the short 
shaft 60 

Teeth in the differen- 
tial wheel . . . .180 

Teeth in the driven 
wheel, on the bobbin 
shaft 42 

Teeth in the wheel to 
which the bobbin is 
made fast . . .- . 40 



54 Teeth in the wheel, on 
the same axis with 
the cone. 

32 Teeth in the wheel that 
takes into the differ- 
ential wheel. 
100 Teeth in the external 
wheel. 



42 Teeth in the di'iving 
wheel, on the bobbin 
shaft. 



Worked out hy Cancellation. 





288-24-6-3 


1-6(0 


20-1 


1-2 


5-1 


1-5-60 


54-9-1 


1-20480 


32 


1-42 


1(00 


1-4(0 


42-1 



32 X 3 



96 



Answer. 



The same without Cancellation. 
Dividend 288 x 20 x 5 x 54 x 32 x 100 x 42 
Divisor . 



= 96 



60x2x60x180x42x40 



Answer. 



BOBBIZSr AJSTD FLY-FKAME. 



93 



From the revolutions per minute of the front-roller, 
and the train of wheels, and the pulley and cone leading 
from the front-roller to the bobbin, find how many revolu- 
tions per minute the bobbin is retarded. 



Worhed out by Cancellation. 




96 


1400 


1004 


1-2 


64 


1-240-60 


54-64 


1-248(0 


32-16-4:-2-l 


142 


1(00 


14(0 


42-1 



96 



Answer. 



The same without Canoellat/ion. 

Dividend 96 x 100 x 5 x 54 x 32 x 100 x 42 . 
Divisor . 



100x2x60x180x42x40 



96 



Answer. 



]N".B. — ^Every time the bobbin is retarded or falls behind 
the spindle one revolution, it laps the roving once round 
the bobbin ; consequently, the front-roller and empty bob- 
bin both being of the same dimensions, the front-roller 
making 96 revolutions per minute, and the bobbin falling 



Oi COTTON MANUFACTUKE. 

behind tlie spindle 96 revolutions per minute, the roving 
will be wound on to the bobbin as fast as it is delivered 
from the front-roller (making no allowance for slirinkage 
in twisting). 

The front-roller wheel has 30 and the change-wheel 32 
teeth, and the back-roller is one inch in diameter. How 
many teeth should there be in the top-camer and the 
back-roller wheel, and what should be the diameter of the 
front-roller to produce a draught of 7 ? 

Worked out. 
30 
32 
8 = I of an inch. 



32 
30 

960 





T680 




7 


A. . . 


10)53760 


B . . 

{Contmued.) 


. 2)5376 



BOBBIN AND FLY-FKAME. 



95 



B . . 


. 2)2688 


B .. . 


. 2)13M 


B . . 


. 7)6Y2 


C . 


. 96)96 




1 


10 Diameter of the fr 



of an inch. 

B. 7x2x2x2 56 Teeth in the back-roller 

wheel. 

C. 96 == 96 Teeth in the top-carrier. 

Answer. 



The front-roller is 1^ and the back-roller one inch in 
diameter. The front-roller wheel has 30, the top-carrier 
96, the change-wheel 32, and the back-roller wheel 56 
teeth. Required the draught. 



Diameter of the back- 
roller, in eighths of 
an inch 8 

Teeth in the change- 
wheel 32 

Teeth in the front-roll- 
er 30 



10 Diameter of the front 
in eighths of an inch. 

56 Teeth in th? back-roUer- 

wlieel. 
96 Teeth in the top-carrier. 



96 COTTON MAJfUFACTUEE. 



Worked out l>y Cancellation. 



1-8 

14-32 

1-3(0 



1(0 

56-7 

96-12-3-1 



Answer. 



The same without Cancellation. 
Dividend 10 x 56 x 96 



Divisor 8 x 32 x 30 

Answer. 

What slioiild be the draught between the middle and 
front rollers, if 19 is drawn into 20 between the back and 
middle rollers, the total draught being Y? 

WorTced out hy Cancellation. 
7 



1-4-20 



19-3.8-.95 



7 X .95 = 6.65 



TTie same without Cancellation. 
Dividend 19 x 7 



Answer. 



= 6.65 



Divisor 20 

Answer. 



BOBBIN AND FLY-FRAME. 



97 



The front-roller is 1:^ and the middle-roller one inch in 
diameter. The front-roller wheel has 30, and the change- 
wheel 35 teeth. How many teeth should there be in the 
top-carrier and the middle-roller wheel to produce a 
draught of 6.65 between the middle and the front rollers? 



Worked out. 
3(0 



i^ of an inch 



1(0 



35 



6.65 



4 of an inch. 



6.65 



B 



B 



53.20 
35 

26600 
15960 

1862.00 
3 

2)5586-00 



3)2T93 



7)931 



{Continued^ 
5 



98 



CO'lTON MAIfUFACTUBE. 



A. 19 X 3 = 

B. 7x7x2 



B ..... 7)133 

, 19)19 

1 

= 57 Teeth in the middle-roller wheel. 

98 Teeth in the top-carrier. 

Answer. 



The front-r. Her is 1^ and the middle-roller one inch in 
diameter. The front-roller wheel has 30, the top-carrier 
98, the change-wheel 35, and the middle-roller wheel 57 
teeth. Required the draught between the middle and the 
front-rollers. 



Diameter of the middle- 
roller, in eighths of 
an inch 8 

Teeth in the change- 
wheel 35 

Teeth in the front-roller 
wheel 30 



10, Diameter of the front- 
roller, in eighths of 
an inch. 

57 Teeth in the middle-rol- 
ler Avheel. 

98 Teeth in the top-carrier. 



Worked out hy Cancellation. 



1-8 
1-7-35 

1-3(0 



1(0 

5741.4-3.8 

98-12.25-1.75 



3.8 X 1.75 



6.65 



Answer. 



BOBBIK AND FLY-FKAIrlE. 



99 



The same without Cancellation. 

Dividend 10 x 57 x 98 . 

Divisor 8 x 35 x 30 



6.65 



Answer. 



From the particulars given, to find the draught between 
the back and the front, and the middle and the front 
rollers, 
die rollers. 



Find the draught between the back and the mid- 



WorTced out hy Ga/nGellation. 



1(0 


84 


1-1.9-5.Y41.4-5Y 


35-54 


1-749-98 


30-1 


1-8 


1(0 


14-32 


56-8-2-1 


1-30 


96-12-6-24.05^ 



1.05tV 



Answer. 



The same without Ca/ncellation. 

Dividend . 8x 35 x30xl0x 56x96 _ 
Divisor . . 10x57x98x8x32x30 



'fF 



Answer. 



100 COTTON MANUFACTURE. 

The draught between the back and the fi'ont-rollers is 
Y, and the dranght between the middle and the front- 
rollers is 6.65. Required the di'aught between the back 
and the middle rollers. 

1-6.65 I 7-lM^ 



^T? 



Answer. 



A Fly-Frame is making coarse roving with a one-inch 
back-roller, a 1^ inch front-roller, a 32 front-roller wheel, 
a 96 top-carrier 40 change-wheel, and a 64 back-roller 
wheel. Eeqnired the dranght. 

Worked out hy Cancellation. 



1-8 

1-32 

1-24(0 



1(0 

96-48-6 

64-2-1 



6 



Answer. 



The same without Ca/ncellation. 

Dividend 10 x 96 x 64 _ ^ 

Divisor 8 x 32 x 40 

Answer. 



BOBBIN AND FLT-FEAME. 



101 



The first layer of roving on the bobbin is 6 inches long, 
containing 30 laps per inch ; consequently, the coppiug- 
rail will have to traverse 6 inches, and the bobbin make 
30 X 6 = 180 revolutions, while winding on the layer, 
and, as has been shown in preceding examples, the empty 
bobbin and the fi'ont-roller are both of the same dimen- 
sions, and in eifect, both move at the same speed, while 
winding on the first layer of roving. The rack to which 
the copping-rail is made fast is driven from, the cone- 
shaft by 5 pairs of wheels, and the wheel that takes into 
the rack. The driven wheels contain respectively, 90, 
100, 60, 80, and 80 teeth, and the rack 4 teeth per inch. 
From the above particulars and the train of wheels, and 
the pulley and cone leading from the front-roller to the 
cone, find driving wheels that will make the copping-rail 
traverse 6 inches, while the fi'ont-roUer makes 180 revo- 
lutions. 



JRevolutions of the front- 
roller 180 

Teeth in the wheel on 
the front-roller , . 100 

Diameter of the pulley 
on the grooved shaft, 
in inches .... 5 



100 Teeth in the wheel on 
the grooved shaft. 
2, Diameter of the small 
end of the cone, in 
inches. 
90 First driven wheel from 
the cone. 



102 



COTTON MANUFACTURE. 



100 Second di-iven wheel 

from the cone. 

60 Third driven wheel 

from the cone. 
80 Fom'th driven wheel 

from the cone. 
80 Fifth driven wheel from 

the cone. 
4: Teeth per inch in the 

rack. 
6 Length of the first lay- 
er, in inches. 



WbrJced out. 



1-2480 

1400 

1-5 



1004 

24 

904 

100-20 

60 

80 

80 

4 

6 



BOBBESr AJSnO FLY-FRAME. 103 



24 



1920 
80 

153600 
60 

9216000 
20 

B 10)184320000 

E . . 10)18432000 

C . . . . . 10)1843200 

A 10)184320 

E . . . , 2)18432 

D 2)9216 

D 4)4608 

D 8)1152 

A 3)144 

3(48 

F . . . . 16)16 

1 



104 



COTTON MANUFACTURE. 



A. 10 X 3 



30 Teetli ia the wheel on the same 



axis with the cone or first driving wheel. 
B. 10 = 10 Teeth in the second driving wheel. 
10 X 3 =: 30 Teeth in the third driving wheel. 
8x4x2 = 64 Teeth in the fourth driving 



C. 
D. 

wheel 
E. 
F. 

rack. 



10 x 2 == 20 Teeth in the fifth driving wheel. 
16 ■ 16 Teeth in the wheel that takes, into the 



Answer. 



From the particulars found in the preceding example, 
find the length of the first layer of roving on the bobbin. 



Worked out ty Cancellation. 




18(0-6 


1-100 


100-1 


1-2 


5-1 


1-3-90 


30-1 


1(00 


1(0 


14-12-60 


3(0-1 


1(0-80 


64-8-2-1 


1-20-80 


20-1 


1-4 


16-4-1 



6 inches. 



Answer. 



BOBBIN AND FLT-FEAME. 



105 



Dividend, 
Divisor, 



The same without Cancellation. 

180 X 100 X 5 X 30 X 10 X 30 X 64 X 20 X 16 



= 6 



100 X 2 X 90 X 100 X 60 X 80 X 80 X 4 

Answer. 



From the particulars found in the preceding example, 
find how many revolutions the front-roller makes while 
the first layer of roving is being wound on to the bobbin. 



Worked out hj Ga/ncellation. 




6-2-1 


14-16 


4-1 


1-20 


80-4-1 


1-24-8-64: 


80-10-24 


1-30 


60-2-1 


1(0 


1(00 


1-3(0 


90 


1-5 


2 


1400 


1004 


90 X 2: 


180 



Answer. 



The 8a/me without Cancellation. 

Dividend, 6 x 4 x 80 x 80 x 60 x 100 x 90 x 2 x 100 _ ^g^ 

Divisor, 16 x 20 x 64 x 30 x 10 x 30 x 5 x 100 

Answer. 
5* 



106 



COTTON MANUFACTURE. 



From the particulars found in tlie preceding example, 
find how many teeth there is in the reversing wheels. 

l!*f.B. — The reversing wheels take into the wheel with 
10 teeth. They are two in nimiber, only one of which is 
in operation at a time. 



Worked out hy Cancellation. 




180-24 


1(00 


100 


1-2 


54 


1-90 


3(0-1 




1(0 


14-20-60 


30-54 


1-240-80 


64-8-2-1 


14-80 


20-1 


14 


16-4-1 


1-6 





100 



Answer. 



The same without Cancellation. 
Dividend, 180 x 100 x 5 x 30 x 10 x 30 x 64 x 20 x 16_ 



Divisor, 



100 X 2 X 90 X 60 X 80 X 80 X 4 x 6 



100 



Answer. 



SPINNING-FEAME. 



107 



SPINNING-FKAME. 

An upright shaft in a spinning-room makes 180 revolu- 
tions per minute, and has on a wheel that takes into a 
wheel with 64 teeth, on a lying-shaft. On the lying-shaft 
there is a pulley that drives a pulley 12 inches in diame- 
ter, on a counter-shaft. On the counter-shaft there is a 
pulley that drives a pulley 8 inches in diameter, on the 
same axis with the cylinder of the spinning-frame. How 
many teeth should there be in the wheel on the upright 
shaft, and what should be the diameter of the driving 
pulleys on the lying and counter shafts, to drive the cylin- 
der 900 revolutions per minute ? 



Revolutions per minute 
of the upright shaft. 180 



900 Revolutions per minute 
of the cylinder. 

64 Teeth in the wheel on 
the lying shaft. 

12, Diameter of the driven 
pulley on the counter- 
shaft, in inches. 
8, Diameter of the pulley 
on the same axis with 
the cylinder, in inch- 
es. 



108 



COTTON MANUFACTUKE. 



Worked out. 



l-3-18(0 



90(0-30 
12-2 



C 



B 
B 



C 



30 

1920 

2 

3840 
8 

10)30Y20 



2)3072 
6)1536 
4)256 
. 8)64 
. 8)8 
1 



A. 10 X 8 
shaft. 



80 Teeth, iii the wheel, on the upright 



SPESTNING-FKAME. 109 

B. 6x4 = 24, Diameter of the pulley on tlie lying 
shaft, in inches. 

C. 8x2 =r 16, Diameter of the driving pulley on 
the counter-shaft, in inches. 

Answer. 

From the particulars found in the preceding example, 
find the revolutions per minute of the cylinder. 



Worked out hy 


Cancellation. 




180-45 


1-2-8-64 


8040 


1-12 


24-24 


1-8 


16-2 


45 X 10 X 


2 900 



The same without Ca/ncellaUon. 
Dividend ... 180 x 80 x 24 x 16 



Answer. 



= 900 



Divisor .... 64 x 12 x 8 

Answer. 

The cylinder makes 900 revolutions per minute, and 
the spindle-warls are one inch in diameter. What should 
be the diameter of the cylinder to di-ive the spindles 6300 
revolutions per minute ? 



110 



COTTON MANUFACTURE. 



Worked out hy Cancellation. 
1-900 I 6300-Y 



7 Answer. 

The cylinder makes 900 revolutions per minute, and on 
the same axis there is a pulley that drives a pulley 15 
inches in diameter, on a stud. On the same axis with the 
pulley on the stud, there is a wheel that, by means of an 
intermediate, takes into a wheel witli TO teeth on the 
front-roller. What should be the diameter of the pulley 
on the same axis with the cylinder, and how many teeth 
should there be in the wheel on the same axis mth the 
pulley on the stud, to drive the front-roller 60 revolutions 
per minute ? 



Revolutions per minute 
of the cylinder . . 900 



60 Revolutions per minute 
of the front-roller. 

15, Diameter of the pulley 
on the stud, in inches. 

TO Teeth in the wheel on 
the front-roller. 



Worked out. 
l-3-9(00 6(0-2 
15-5 

T(0 
{Continued^ 



SPmNING-FKAME. Ill 

5 

35 

2 

A . . . Y)YO 

A . . . 2)10 

B . . . 5)5 

1 

A. 7x2 = 14 Teetli in the wheel on the same axis 
with the pulley on the stud. 

B, 5 = 5, Diameter of the pulley on the same axis 
with the cylinder, in inches. 

Answer. 

From the particulars found in the preceding example, 
find the revolutions per minute of the front-roller. 

Worked out hy CanoellaUon. 
900-60 



145 

i44:-ro 



54 
144 



60 



Answer. 



112 COTTON MAITOFACTUKE. 

The sa/me witJiout Ca/ncellation. 
Dividend 900 x 5 x 14 



60 



Divisor 70 x 15 

Answer. 

The front-roller is one incli in diameter, and makes 60 
revolutions per minute, and the spindles make 6300 revo- 
lutions per minute. Required the number of tm-ns of 
twist per inch in the yarn. 

Worked out hy CetnceUation. 

1-6(0 I 630(0405-8.Y5-33.42 
1-.2618-3.1416 I 

33.42 

Answer. 



The same without Cancellation. 
Dividend 6300 



33.42 



Divisor 3.1416 x 60 

Answer. 

The cylinder is 1 inches in diameter, and on the same 
axis there is a pulley 5 inches in diameter that drives a 
pulley 15 inches in diameter, on a stud. On the same axis 
with the pulley on the stud, there is a wheel with 14 teeth 



SPrNTNING-FKAME. 



113 



that, by means of an intermediate, takes into a wheel 
with YO teeth, on the front-roller. Kequired the number 
of tm-ns of twist per inch in the yarn, the front-roller 



being one inch in diameter. 



Diameter of the front- 
roller, in inches . . 1 

Circumference . . 3.1416 

Diameter of the pulley 
on the same axis with 
the cylinder, in inches 5 

Teeth in the wheel on 
the same axis with 
the pulley on the stud 14 



7, Diameter of the cylin- 
der, in inches, 

16, Diameter of the pulley 
on the stud, in inches. 

YO Teeth in the wheel on 
the front-roller. 



Worlced out hy Ca/riGellation. 



1-.4488-3.1416 

1-5 

144 



1-1 

15-33.42 
Y0-.144 



33.42 



Answer. 



The, same without Cancellation 
Dividend . . . . Y X 15 x YO 



Divisor 3.1416 x 5 x 14 



= 33.42 



Answer. 



114 



COTTON MANUFACTURE. 



The heart or traverse motion makes one revolution 
while two layers of yarn are being wound on the bobbin. 
On the same axis with the heart there is a wheel with 72 
teeth driven by a worm. On the same axis with the 
worm there is a pulley 9 inches in diameter, driven from 
a pulley on a stood. On the same axis with the pulley on 
the stood there is a wheel with 32 teeth that takes into a 
wheel on the front-roller. How many teeth should there 
be in the wheel on the front-roller, and what should be 
the diameter of the pulley on the stood, to make each 
layer of yarn 15 yards long, the front-roller being one inch 
in diameter, making no allowance for shrinkage in twist- 
ing? 



Layers wound on while 
the heart makes one 
revolution .... 

The worm is equal to 
one tooth, in effect . 



1 Kevolutions of the heart. 



72 Teeth in the wheel on 
the same axis with 
the heart. 
9, Diameter of the pulley 
on the same axes with 
the worm, in inches. 

32 Teeth in the wheel on 
the same axis with 
the pulley on the 
stud. 



SPINNING-FEAME. 



115 



Indies in one yard 



36 



Length of one layer of 
yarn, in yards ... 15 



1, Diameter of the front- 
roller, in inches. 
3.1416 Ratio of circnmfer- 
ence to diameter. 



Worked out. 


1-2 


1 


1 


Y2-6-24 




9-3 




32 


1-3-36 


1 




3.1416'.62832 


1-345 







.62832 




32 




125664 




188496 




20.10624 




3 


A 


2)60.31872 


A .... . 

{Continued^ 


3)30.15936 



116 COTTON MANUFACTURE. 

A .... . 4)10.05312 



B . . 2.51328)2.51328 



A. 2 X 3 X 4 — —24 Teeth in tlie wheel on the 
front-roller. 

B. 2.51328 2.51328, Diameter of the puUey on 

the stood, in inches. 

Answer. 

rrom the particulars found in the preceding example, 
find the number of yards in one layer of yarn. 

Worked out hy Ccmcellation. 



1-2 


1 


1 


Y2-6-2-1 


1-2.51328 


9-3 


1-3-24 


32-4 


1-3-36 


1 




3.1416-1.25 



1.25 X 4 X 3 = 15 Answer. 



The same without Ca/riGellation. 
Dividend . . . T2 x 9 x 32 x 3.1416 



= 15 



Divisor .... 2 x 2.51328 x 24 x 36 

Answer. 



MASOiST S MULE. 



117 



MASON S MULE. 

An npriglit sliaft in a mule-room makes 180 revolutions 
per minnte, and has on a wheel that takes into a wheel 
with 60 teeth, on a lying-shaft. On the lying-shaft there 
is a pulley that drives a pulley 12 inches in diameter, on 
the twist-shaft. How many teeth should there be in the 
wheel on the upright shaft, and what should be the diame- 
ter of the pulley on the lying-shaft, to drive the mule 
SI' stretches per minute, the twist-shaft making 75 revolu- 
tions per stretch, and the time occupied in drawing out 
and twisting being three-quarters of the time necessary to 
perform the whole stretch ? 

IT.B. — The twist-shaft makes from one to three revolu- 
tions, according to the size of the cop, while taking in the 
carriage, but there is a loss of about that amount while 
falling from the maximum to the minimum speed neces- 
sary for backing off. 



Revolutions per minute 
of the upright shaft 180 

Time necessary for 
drawing out and 
twisting 3 



Y5 Revolutions per stretch 
of the twist-shaft. 
4: Time necessary to per- 
form the whole 
stretch. 

60 Teeth in the wheel on 
the lying-shaft. 



113 



COTTON MANDFACTrKK 





12, Diameter of tlie pulley 




on the twist-shaft, in 




inches. 




3,5 Stretches per minute. 


Worked out. 


1-3480 


75-25 


1-3 


4 




604 




124 




3.5 


25 


4 


100 


4 


400 


3.5 


2000 


A . . . 


1200 


. 7)1400.0 


A 10)200 


B. . . . . 20)20 




1 



mason's aroLE. 119 

A. 10 X 7 = 70 Teetli in the wheel on the upright 
shaft. 

B. 20 20, Diameter of the pulley on the lying- 
shaft, in inches. 

Answer. 

From the particulars found in the preceding example, 
find how many stretches per minute the mule will make. 

Worked out hy Cancellation. 



1-545-75 

1-60 

1442 

14 



180-34 
7047.5-3.5 
20-54 
3-1 



3.5 



Answer. 



The sarne without CoMcellation. 
Dividend . . . . 180 x 70 x 20 x 3 



= 3.5 



Divisor 75 x 60 x 12 x 4 

Answer. 

The cam that permits the belt to pass from the fast to 
the loose pulley makes one revolution per stretch. On 
the same axis with the cam there is a wheel that takes 
into a wheel with 36 teeth on the worm-wheel-shaft. On 



120 



COTTON MANITFAOTUKE. 



tlie worm-wlieel-sliaft there is also a wheel that takes into 
a worm on the twist-shaft. How many teeth should there 
be in the wheel on the cam-shaft, and the wheel that takes 
into the worm, to permit the twist-shaft to make Y5 revo- 
lutions per stretch ? 

Worked out. 

75 Revolutions per stretch 
of the twist-shaft. 

36 Teeth in the driving 
wheel on the worm- 
wheel-shaft. 



B 



75 
36 

450 

225 

5)2700 



A 5)540 

A 3)108 

A 3)36 

B 3)12 

B 4)4 

1 



mason's mule. 121 

A. 5x3x3 = 45 Teeth in the wheel that takes 
into the worm. 

B. 5x3x4 = 60 Teeth in the wheel on the cam- 
shaft. 

Answer. 

From the particulars found in the preceding example, 
find how many revolutions the twist-shaft makes per 
stretch. 

Worked out hy Cancellation. 
4545 



1-3-36 



60-5 



15 X 5 = 75 Answer. 



The same without Cancellation. 
Dividend . . . . . . . . 45 x 60 



75 



Divisor 36 

Answer. 

The twist-shaft has on a wheel with 21 teeth that, by 

means of an intermediate, takes into a wheel on the 

front-roller. How many teeth are there in the wheel on 

the front-roller, if 68 revolutions of the twist-shaft turn 

out 59.816064 inches, the front-roller being one inch in 

diameter ? 

6 



122 



COTTON MANUFACTUKE. 



Length turned out, in 



inches 



59.816064 



68 Revohitions of the 

twist-shaft. 
21 Teeth in tlie wheel on 
the twist-shaft. 
1, Diameter of the front- 
roller, in inches. 
3.1416 Circumference. 



Worked out hy Cancellation. 



l-.284.r6-9.5249.04-59.816064 



68-34-1Y4 
21-75 
1 
3.14164 



75 



Answer. 



The same without Cancellation. 

Dividend 68 x 21 x 3.1416 . 

Divisor 59.816064 



75 



Answer. 



The wheel that takes into the worm has 45 teeth. On 
the same axis with this wheel there is a wheel with 36 
teeth that takes into a wheel with 60 teeth, on the cam- 
shaft. The spindle-warl is one inch, and the twist-pulley 



MASON S MULE. 



123 



17 inclies in diameter, and the length of the stretch is 
59.816064: inches. Kequired the twist per inch in the 
yarn. 



Teeth in the wheel on 
the same axis with 
the wheel that takes 
into the worm 

Diameter of the spindle 
warl, in inches . . 

Length of the stretch, 



36 



in inches 



59.816064 



45 Teeth in the wheel that 
takes into the worm. 

60 Teeth in the wheel on 
the cam-shaft. 



IT, Diameter of the twist- 
pulley, in inches. 



Worked out iy Ccmcellation. 
45-15-21.31 + 



1-3-36 
1 

l-.'r037184-3.518592-59.816064 



60-5-1 
IM 



Answer. 



21.31 + 

The saTYie without Ca/ncellation. 
Dividend . . . . 45 x 60 x 17 



Divisor 36 x 59.816064 



= 21.31 + 



Answer. 



124 



COTTON MANUFACTUEE. 



The Mason's Mule is so constructed as to take in and 
out the carriage by means of a spur-wheel and chain. 
The wheel has a certain number of spurs, and each spur 
takes into a link in the chain, and, taken together, they 
are, in effect, equal to a pulley and band 3 inches in effect- 
ive diameter. On the same axis with the spur-wheel (the 
back shaft), there is a wheel di'iven fi-om a wheel with 28 
teeth, on an intermediate shaft. On the intermediate 
shaft there is also a wheel driven from a wheel with 30 
teeth on the same axis with the front-roller. How many 
teeth are there in the wheel on the back shaft, and the 
driven wheel on the intermediate shaft, if the surface 
velocity of the front-roller and the traverse of the carriage 
are equal, the front-roller being one inch in diameter ? 



Worked out. 



Diameter of the front- 
roller, in inches . . 



28 Teeth in the driving 
wheel, on the inter- 
mediate shaft. 

30 Teeth in the wheel on 
the same axis with 
the front-roller. 
3, Effective diameter of the 
spur-wheel and chain, 
in inches. 



mason's mule. 125 



28 
30 



840 
3 

A 12)2520 

A 6)210 

B 35)35 

1 

A. 12 X 6 Y2 Teeth in the driven wheel, on the 

intermediate shaft. 

B. 35 = 35 Teeth in the wheel, on the back shaft. 

Answer. 

From the particulars found in the preceding example, 
find how many inches the carriage will be taken out while 
the rollers deliver 59.816064 inches. 



Worked out hy Cancellation. 




59.816064 


1-342-Y2 


30-54 


1-5-35 


28-Y4 




34 


59.81 


6064 



Answer. 



126 COTTON MANUFACTTJRE. 

Xlie same without Cancellation. 

Dividend . 59.816064 x 30 x 28 x3 _ ^^ ^^^^^^ 
Divisor . . 7-2 x 35 

Answer. 

The wheel on the front-roller for taking ont the carriage 
has 30 teeth, and the rollers deliver 59.816064 inches per 
stretch. How many inches will the rollers deliver with a 
wheel with 32 teeth ? 

Worked out hy Oa/nceTlaUon. 

59.81606444.954016 
1-4-32 30-3.75 

14.954016 X 3.75 = 56.07756 

Answer. 

The sa/me without Cancellation. 

Dividend . . . 59.816064 x 30 _ ^^ ^^^^g 
Divisor .... 32 

Answer. 

The front-roller delivers 56.07756, and the length of the 
stretch is 59.816064 inches. How many inches does the 
carriage gain per stretch ? 



mason's mule. 127 

59.816064 

56.077560 



3.738504: 



Answer. 



From tlie particulars found in tlie preceding example, 
find the draught at the carriage. 

Worked out hy Cancellation. 
1-66.07766 I 59.816064:-1.06 

1.06 

Answer. 

The spm'-wheel on the back shaft, and the chain by 
which the carriage is taken in and out are, in effect, equal 
to a pulley and band 3 inches in effective diameter. On 
the back shaft there is a wheel that takes into a wheel 
with 168 teeth, on an intermediate shaft. On the inter- 
mediate shaft there is a wheel that takes into the bottom 
sliding-rack. The relative velocity of the bottom to that 
of the top sliding-rack is as 5 to 4. On a second inter- 
mediate shaft there is a wheel with 21 teeth that takes 
into the top sliding-rack. On this shaft there is also a 
wheel that takes into a wheel with 24 teeth, on the same 
axis with the twist-pulley. How many teeth should there 
be in the whee] on the back shaft, the wheel that takes 



128 



COTTON MANUFACTUEE. 



into the bottom sliding-rack, and the wheel on the second 
intermediate shaft that takes into the wheel on the same 
axis with the twist-pulley ; and what should be the diame- 
ter of the twist-pulley and the spindle, to give the bare 
spindle a sm-face velocity equal to the velocity of the 
carriage while going in, the spindle-warl being one inch in 
diameter ? 

N.B. — There is nothing between the twist-pulley and 
the spindle-warl that needs to be taken into consideration 
in solving the above problem. 

3, Effective diameter of 
the spur-wheel and 
chain, in inches. 
168 Teeth in the wheel that 
takes into the wheel, 
on the back shaft. 
21 Teeth in the wheel that 
takes into the top 
sliding-rack. 
24: Teeth in the wheel on 
the same axis with 
the twist-pulley. 
1, Diameter of the spin- 
dle-warl, in inches. 
5, Relative velocity of the 
bottom sHding-rack. 



Relative velocity of the 
top sliding-rack . . 



mason's mule. 



129 



Worked out. 
3 

168 
21 
24-6 
1 
5 



14 



168 
3 

504 
21 

504 
1008 





10584 




6 




63504 




5 


E . 


. .5)317520.0 


E . 


. .5)635040.0 


D . . 


. 7)1270080 




. . 7)181440 


tntvnued.^ 





130 COTTON MANUFACTURE. 

C . . . . . 12)25920 



A 5)2160 

D 2)432 

C 8)216 

B 2T)27 

1 

A. 7x6 = 35 Teetli in the wheel on the back shaft. 

B. 2Y 27 Teeth in the wheel that takes into the 

bottom shding-rack. 

C. 12 X 8 = 96 Teeth in the wheel on the second 
intermediate shaft, that takes into the wheel on the same 
axis with the twist-pulley. 

D. 7x2 == 14, Diameter of the twist-pulley in 
inches. 

E. .5 X .5 = .25, Diameter of the spindle, in inches. 

From the particulars found in the preceding example, 
find how much yarn will be wound on to the bare spindle 
whUe the spur-wheel takes in 59.816064 inches of chain. 

Worked out lyy Cancellation. 

59.816064 
1-342-3 .254 
144468 35-74 
{Continued.) 



MASON'fi 


MULE. 




2T-9-3-1 


1-5 


4-1 


1-3-21 




1-3-24: 


96-84 


1 


144 


59.816064 inches. 



131 



Answer. 



Div. 



The same without Cancellation. 
59.816064 X .25 x 35 x 27 x 4 x 96 x 14 



Divisor, 



3 X 168 X 5 X 21 X 24 



= 59.816064 
Answer. 



From the particulars found in the preceding example, 
find how many inches of chain will be taken in per 
stretch of 59.816064 inches. 



Worlced out hy Cancellation. 



1-.25 

1-5-35 

1-3-9-2T 

14 

1-8-96 
144 



59.816064 

34 

168444 

5-20-54 

21-M 

24-34 



59-816064 



Answer. 



132 



COTTON MANUFACTURE. 



The same without Cancellation. 

Dividend, 59.816064 x 3 x 168 x 5 x 21 x 24 _ ^^ 8igo64 
Divisor, .25 X 35 X 27 X 4 X 96 X 14 

Answer. 

From the particulars found in the preceding example, 
find the diameter of the twist-pulley. 

Worked out hy Cancellation. 





1 




l-7'35 


16844 




1-.25 


3-1 
21-3-1 




1-4 


5-1 




1-3-9-27 






1-8-96 


24-342-3-1 




14 inches. 


Answer. 


The same rDithoxvt Cancellation. 




Dividend . .168x3 
Divisor . . . 35 x .25 


X 21 X 5 X 24 -, . . , 

— 14 inches. 

x4x27x96 



Answer. 



From the particulars found in the preceding example, 
find the diameter of the spindle. 



MASON S MULE. 



133 



Worked out lyy Ccmcellation. 




34 




21-74 


14 


54 


1-3-9-2Y 




1-8-96 


24-34 


1-5-35 


168-14-1 


144 


1-.25 



.25 = 1^ of an inch. 

The same wiiJiout Cancellation. 
Dividend . . 3 x 21 x 5 x 24 x 168 . 
Divisor . . . 4 x 27 x 96 x 35 x 14 



Answer. 



.25 



Answer. 

How many revolutions must the spindle make to wind 
the yam on to the bare spindle while the carriage is going 
in, the diameter of the spindle being a quarter of an inch, 
and the length of the stretch 59.816064 inches ? 



Worked out 'by Cancellation. 



1-.25 
1-3.1416 



59.816064-19.04-76.16 



76.16 



Answer. 



134 



COTTON MANUFACTURE. 



The same without Cancellation. 
Dividend 59.816064 



Divisor 3.1416 x .25 



= 76.16 



Answer. 



Find how many inches of chain the spur-wheel will take 
in, while the spindle makes 76.16 revolutions.^ 



Worked out hy Cancellation. 




76.1649.04 


144 




1-8-96 


24-34 




21-74 


1-4 


54 


1-3-9-27 




1-5-35 


168-144 




34 




3.1416 



3.1416 X 19.04 = 59.816064 



Answer. 



The same without Cancellation. 
Div., 76.16 X 24 X 21 X 5 X 168 X 3 X 3.1416 _ ^^ §16064 



Divisor, 



14x96x4x27x35 



Answer. 



mason's mule. 



135 



The leugtK of the cop is regulated more or less by the 
eopping-rail and shaper, and not wholly by the length of 
traverse of the nut on the screw in the recess of the 
builder. It is found by observation that a well propor- 
tioned and well built cop, having on 630 stretches of l^o. 
40 filling, will measure from extreme point to extrenie 
point, as much more than the traverse of said nut, as 19 
is more than 14. On the same axis with the screw in the 
recess of the builder, there is a wheel that takes into a 
wheel with 2Y teeth. On the same axis with the latter 
wheel there is a spur-wheel that moves one spur per 
stretch. How many threads per inch are there in the 
screw ; how many teeth in the wheel on the same axis 
with the screw ; how many spm*s in the spur-wheel, and 
what is the length of the cop, if it contains 630 stretches, 
and the traverse of the nut on the screw in the recess 
of the builder, is to the length of the cop as 14 to 19 ? 



Proportionate length of 
traverse of the nut in 
the recess of the 
builder 14 



630 Stretches on the cop. 
27 Teeth in the wheel that 

takes into the wheel 

on the same axis with 

the screw. 
19, Proportionate length 

of the cop. 



136 



COTTON MANUFACTURE. 



Worked out. 

630-9045 

2Y 
1-244 19 



45 

27 



315 
90 





1215 




19 




10935 




1215 


A . . . 


. 3)23085 


B . . 


6)7695 


C . . 


. 3)1282.5 


C . . 


. 3)427.5 


B. . . 


. 10)142.5 


A . . . 


. 3)14.25 


D . 


. 4.76)4.75 



mason's mule. 137 

A. 3x3 = 9 Threads per inch in the screw. 

B. 10 X 6 == 60 Teeth in the wheel on the same 
axis with the screw. 

C. 3x3 zi=:= 9 Spurs in the spur-wheel, 

D. 4.75 4.75, The length of the cop, in inches. 

Answer. 

From the particulars found in the preceding example, 
find the length of the cop, in inches. 

WorTced out lyy Cancellation. 



1-9 


63(0-9-l 


l-2-6(0 


27-94.54 


1-244 


19-9.54.75 


1-2-9 





4.75 

TJie same without CaMcellation. 
Dividend . . . . . 630 x 27 x 19 



Answer. 



4.75 



Divisor 9 x 60 x 14 x 9 

Answer. 

From the particulars found in the preceding example, 
find the number of stretches on a cop. 



138 



COTTON MANUFACTUKE. 



Worked out hy CanGellation. 




4.754 




9-3 


1-3-27 


6045 




94 


14.7549 


14 



15 X 14 X 3 



630 



Answer. 



The same without Ca/rhcellation. 
Dividend . . 4/r5 x 9 x 60 x 9 x 14 
Divisor . . . 



= 630 



27 x 19 



Answer. 



From the particulars found in the preceding example, 
find the number of threads per inch in the screw. 



Worked out hy CanGellation. 


1-4.75 






63(0-7-1 


l-3-6(0 


27-9 


1-9 




1-244 


19-4-24 



Answer. 



MASON S MULE. 



139 



The sa/me witliout Ccmcellation. 
Dividend 630x27x19 



9 



Divisor 4.75x60x9x14 

Answer. 



From tlie particulars found in the preceding example, 
find the number of teeth in the wlieel on the same axis 
with the screw. 



Worlced out ly Cancellation. 




630-7040 


1-9 






27-3 


1-9 




1-244 


194-2 


14.Y5 




10 x 3 X ^ 


>. 60 



Answer. 



The sa/me without Cancellation. 

Dividend 630 x 27 x 19 

Divisor 



= 60 



9 X 9 X 14 X 4.75 

Answer. 



The back-roller is seven-eighths of an inch in diameter. 
The front-roller wheel has 30, and the change-wheel 36 



140 COTTON MAJSTDFACTURE. 

teeth. How many teeth should there be in the top-carrier 
and the back-roller wheel, and what should be the diame- 
ter of the front-roller to produce a draught of 9 ? 

Worked out. 

7, Back-roller in eighths 
of an inch. 
30 Teeth in the front-roller 

wheel. 
36 Teeth in the change- 
wheel. 
9, Draught. 



36 
30 





1080 




7 




T560 




9 


A . . . 


. 4)68040 


A . . . 


2)17.010 


B . . 


. . 5)8505 


B . . 


. . 3)1701 



(Continued.) 



mason's mule. 14:1 

B . . . . Y)567 

C. . . . 81)81 

1 

A. 4x2 == 8, Diameter of the fi'ont-roUer, in eighths 
of an inch. 

B. 5x3x7 = 105 Teeth in the top-carrier. 

C. 81 == 81 teeth in the back-roller wheel. 

Answer. 

From the particulars found in the preceding example, 
find the di'aught between the back and the front rollers. 

Worked out hy Ccmcellation. 



1-7 
1-2-30 
1-9-36 



844 
105454 

81-9 



Answer. 



The sa/me without Cancellation. 
Dividend . . . . . . . 8x105x81 



= 9 



Divisor 7x30x36 

Answer. 



142 



COTTON MANUFACTURE. 



THE FKANE.LIN MULE, 



A mule is driven from an upright shaft making 180 
revolutions per minute, by a train of three pairs of pul- 
leys, and one pair of wheels. The driven wheel has 64 
teeth, and the respective diameters of the driven pulleys 
are 20, 18, and 12 inches. How many teeth should there 
be in the driving wheel, and what should be the respective 
diameters of the driving pulleys, to drive the mule S^ 
stretches per minute, the twist-shaft making 72 revolutions 
per stretch, and the time occupied in drawing out and 
twisting being three-quarters of the time necessary to 
perform the whole stretch ? 



Revolutions of the up- 
right shaft per minute, 180 

Time occupied in draw- 
ing out and twisting, 3 



72 Revolutions of the twist- 
shaft per stretch. 

3.25 Stretches per minute. 
4 Time occupied in per- 
forming the whole 
stretch. 

64 Teeth in the diiven wheel. 

20, Diameter of the first 
driven pulley, in inch- 
es. 

18, Diameter of the second 
driven pulley, in inch- 
es. 



THE FRANKLIN MULE. 



143 



12, Diameter of the third 
driven pulley (which 
is on the twist-shaft), 
in inches. 



Worked out. 



148(0 



1-3 



72-24 

3.25 

4 

64 

2(0 

184 

12 



{Continued.) 



3.25 
24 

1300 
650 

78.00 
4 

312 
64 



1248 

1872 



144 



COTTON MANUFACTURE. 







19968 






2 






39936 






12 






T98Y2 






39936 


A 


. . . 


12)479232 


A 


. . . 


. 6)39936 




D . 


. . 8)6656 




C . . 


. . 2)832 

. . 2)4:16 


C . . 

B. . . 


. . 10)208 
. 20.8)20.8 



A. 12 X 6 72 Teeth, in the driving wheel. 

B. 20.8 == 20.8, Diameter of the first driving pulley, 
in inches. 

C. 10 X 2 ^= 20, Diameter of the second driving pul- 
ley, in inches. 

D. 8x2 : 16, Diameter of the third driving pulley, 

in inches. 

Answer. 



THE FBANKLIN MULE. 



145 



A mule is driven from an upright shaft making 180 
revolutions per minute, by a train of three pairs of pul- 
leys and one pair of wheels ; the driving wheel has Y2, 
and the driven wheel 64 teeth. The respective diameters 
of the driving pulleys are 20.8, 20, and 16, and the driven 
pulleys 20, 18, and 12 inches. How many stretches per 
minute does the mule make, allowing the last driven pul- 
ley (which is on the twist-shaft), to make Y2 revolutions 
per stretch, and the time occupied in drawing out and 
twisting being three-quarters of the. time necessary to 
perform the whole stretch ? 



Revolutions of the twist- 
shp-ft per stretch , . 



Y2 



Time occupied in per- 
forming the whole 
stretch 4 

Teeth in the driven 
wheel 64 

Diameter of the first 
driven pulley, in inch- 
es 20 

Diameter of the second 
driven pulley, in inch- 
es 18 



180 Revolutions of the up- 
right shaft per min- 
ute. 
3, Time occupied in draw- 
ing out and twisting. 

Y2 Teeth in the driving 
wheel. 
20.8, Diameter of the first 
driving pulley, in 
inches. 
20, Diameter of the second 
driving pulley, in 
inches. 



146 



COTTON MAJSTUFACTUBE. 



Diameter of the third 
di'iven pulley (which 
is on the twi&t-shaft), 
in inches .... 



12 



16, Diameter of the third 
driving pulley, in 
inches. 



Worked out hy Cancellation. 


1-Y2 


18(0-1 


14 


34 


1-8-64 


72-1 


■ 1-2(0 


20.8-2.6 


148 


20-10-1.25 


1-342 


16-4-1 



2.6x1.25 



3.25 



Answer. 



T%e same without Cancellation. 
Dividend . 180 x 3 x Y2 x 20.8 x 20 x 16 . 
Divisor . . 72x4x64x20x18x12 



3.25 



Answer. 



The twist-pulley is 17 inches in diameter, makes 72 
revolutions per stretch, and drives the pulley on the drum- 
shaft. On the drum-shaft there is a wheel with 50 teeth 
that takes into a wheel on the same axis with the di'um ; 
the drum is 10 inches in diameter, and drives the spindles. 
How many teeth should there be in the wheel on the same 



THE FKANKLIN MULE. 



147 



axis with the drum ; what should he the diameter of the 
pulley on the drmn-shaft, and the spindle-warl, and what 
should be the length of the stretch to put 20 turns of 
twist per inch into the jam ? 



Tm*ns of twist per inch 
in the yarn ... 20 



72 Revolutions per stretch 
of the twist-pulley. 

17, Diameter of the twist- 
pulley, in inches. 

50 Teeth in the wheel on 
the di'um-shaft. 

10, Diameter of the drum 
in inches. 



Worked out. 

72-36 
17 

50 



1-2(0 



1(0 



36 
17 



{ContMiued.) 



148 COTTON MANUFACTURE. 



252 
36 

612 

50 



A . . . . 10)30600 
B. . . . 10)3060 
B . . . . 2)306 

B 3)153 

C . . . . 51)51 
D . . . . 1 



A. 10 == 10, Diameter of the pulley on the di'um- 
shaft, in inches. 

B. 10 X 2 X 3 60, Length of the stretch, in inches. 

C. 51 ■ 51 Teeth in the wheel on the same axis 
with the drum. 

D. 1 == 1, Diameter of the spindle-warl, in inches. 

Answer. 

The twist-pulley makes 72 revolutions per stretch, is 17 
inches in diameter, and di'ives the pulley on the drum- 
shaft which is 10 inches in diameter. On the drum-shaft 
there is a wheel with 50 teeth that takes into a wheel 
with 51 teeth, on the same axis with the drum. The 



THE FRANKLIN MULE. 



149 



drum is 10 inches in diameter and drives tlie spindles, the 
warls of which is one inch in diameter. How many turns 
of twist per inch is there in the yarn, the length of the 
stretch being 60 inches ? 







72 Revolutions per stretch 






of the upright shaft. 


Diameter of the pulley 




17, Diameter of the twist- 


on the drum-shaft, in 




pulley, in inches. 


inches 


10 




Teeth in the wheel on 




50 Teeth in the wheel on 


the same axis with 




the di'um-shaft. 


the drum .... 


51 




Diameter of the spindle- 




10, Diameter of the drum, 


warl, in inches . . 


1 


in inches. 


Length of the stretch, 






in inches .... 


60 





Worked out hy Ccmcellation. 
Y2424 



1(0 

147-51 

1 

1-6(0 

5x4 = 



IM 

5(0 
1(0 



20 



Answer. 



150 



COTTON MANUFACTURE. 



= 20 



The same without Ca/ncellation. 

Dividend. ..... 72x17x50x10 

Divisor 10x51x60 

Answer. 

The twist-sliaft makes 68 revolutions per stretch v^hile 
in connection with the rollers, and has on a wheel with 18 
teeth that, by means of an intermediate, takes into a 
wheel on the roller-shaft. On the other end of the roller- 
shaft, there is a wheel with 40 teeth that takes into a 
wheel on the front-roller. How many teeth should there 
be in the driven wheel on the roller-shaft, and the wheel 
on the front-roller, to turn out 60.0831 inches per stretch, 
the front-roller being one inch in diameter ? 



68 Revolutions per stretch 
of the twist-shaft while 
in connection with the 
rollers. 

18 Teeth in the wheel on 
the twist shaft. 

40 Teeth in the wheel on 
the roller-shaft that 
takes into the wheel 
on the front-roller. 



THE TBANKLIN MULE. 



151 



Length, turned out per 
stretch, in inches, 60,0831 



1, Diameter of the froUer, 
in inches. 
3.1416, Circumference. 



Worked out. 




68-32 




18-2 




40 


1-2.12649.125-60.0831 


1 




3.1416-1 



32 
2 

64 
40 



A 
A 
A 
A 



B 



4)2560 
2)640 
4)320 

. 2)80 

40)40 

1 



A. 4x2x4x2 
the roller-shaft. 



64 Teeth in the driven wheel on 



152 



COrrON ]\tANUFACTURE. 



B. 40 40 Teeth in the wheel on the front- 
roller. 

Answer. 

The twist-shaft makes 68 revolutions per stretch while 
in connection with the rollers, and has on a wheel with 18 
teeth that takes into a wheel with 64 teeth, on the roUer- 
sliaft. On the other end of the roller-shaft there is a 
wheel with 40 teeth, that takes into a wheel with 40 
teeth, on the front-roller. How many inches will be 
tm'ned out per stretch, the front-roller being one inch in 
diameter ? 



Teeth in the driven 
wheel on the roller- 
shaft ..,-... 64 

Teeth in the wheel on 
the front-roller . . 40 



68 Revolutions per stretch 
of the twist-shaft while 
in connection with the 
rollers. 

18 Teeth in the wheel on 
the twist-shaft. 

40 Teeth in the driving 
wheel on the roller- 
shaft. 
1, Diameter of the front- 
roller, in inches. 
3.1416 Circumference. 



THE FEANKLIN MULE. 153 

Worked out hy Cancellation. 

68-17 



1-846-64 
140 



18-9 

404 

1 

3.1416-.3927 



17 X 9 X .3927 = 60.0831 . Answer. 

The same without CanGellation. 
Dividend . . . 68 xl8 x40x3.1416 _ ^^ ^gg^ 

Answer. 



Divisor "... 64x40 



The front-roller is one inch in diameter, and has on a 
wheel that takes into a wheel with 40 teetli, on the roller- 
shaft. On the other end of the roller-shaft there is a 
wheel that takes into a wheel with 64 teeth, on the draw- 
ing-out shaft. On the other end of the drawing-out shaft 
there is a wheel that takes into a wheel with 40 teeth, on 
the scroll-shaft. How many teeth should there be in the 
wheel on the front-roller, the wheel on the roller-shaft 
that takes into the wheel on the drawing-out shaft, and 
the wheel that takes into the wheel on the scroll-shaft ; 
and what should be the diameter of the scroll to give it a 

surface velocity equal to that of the front-roller ? 

7* 



154 



COTTON MANUFACTUKE. 



40 Teeth in the wheel on 
the roller-shaft tliat 
takes into the wheel 
on the front-roller. 

64 Teeth in the wheel on 
tlie drawing-out shaft 
that takes into the 
wheel on the roller" 
shaft. 

^0 Teeth in the wheel on 
the scroll-shaft. 
1, Diameter of the front- 
roller, in inches. 





Worked 


out. 

64 
40 

2560 




. . . 


40 




10)102400 


A 


. . . . 


10)10240 


A 


.... 


. 2)1024 


A 


.... 


. 2)512 


{^Continued.) 





THE FKANKLESr MTJLE. 



155 



c . . . 


. 2)256 


B . . . 


. 2)128 


B . . . 


2)64 


B . . . 


2)32 


B ... 


2)16 


B . . . 


. . 2)8 


D . . 


. . 2)4 


D . . 


. . 2)2 




1 


A. 10 X 2 X 2 40 Teeth ] 


Ln the wheel on the front- 


roller. 




B. 2x2x2x2x2 32 I 


'eeth in the wheel on the 



roller-shaft, that takes into the wheel on the drawing-out 
shaft. 

C. 10 X 2 : 20 Teeth in the wheel that takes into 

the wheel on the scroll-shaft. 

D. 2x2 =^ 4, Diameter of the scroll, in inches. 

Answer. 

The front-roller is one, and the scroll is 4 inches in 
diameter. The front-roller has on a wheel with 40 teeth 
that takes into a wheel with 40 teeth, on the roller-shaft. 
On the other end of the roller-shaft there is a wheel with 
32 teeth that takes into a wheel with 64 teeth, on the 



156 



COTTON MANUFACTURK. 



di'awing-out shaft. 



On the otlier end of the drawing-out 



shaft there is a wheel with 20 teeth that takes into a wheel 
with 40 teeth, on the scroll-shaft. What is the surface 
velocity per stretch of the scroll, if that of the front-roller 
is 60.0831 ? 

!N^.B. — In practice it is necessary to add the diameter 
of the drawing-out band to that of the scroll. 

60.0831, Surface velocity per 
stretch of the front- 
roller. 
Diameter of the front- 4,. Diameter of the scroll, 

roller, in inches . . 1 in inches. 

Teeth in the wheel on 40 Teeth in the wheel on 

the roller-shaft, that the front-roller. 

takes into the wheel 

on the front-roller . 40 
Teeth in the wheel on 

the drawing-out shaft 

that takes into the 

wheel on the roller- 
shaft 64 

Teeth in the wheel on 

the scroll-shaft . . 40 



32 Teeth in the wheel on 
the roller-shaft, that 
takes into the wheel 
on the drawing-out 
shaft. 

20 Teeth in the wheel on 
the drawing-out shaft, 
that takes into the 
wheel on the scroll- 
shaft. 



THE FEANKLm MULE. 



157 



Worked out hy Cancellation. 




60.0831 


1 


44 


140 


404 


1-2-64 


324 


14(0 


2(04 



60.0831 



Answer. 



Dividend 
Divisor . 



The same witliout Cancellation. 
60.0831 X 4 X 40 X 32 X 20 



40 X 64 X 40 



60.0831 
Answer. 



The spindle is g^, the spindle-warl is one, and the drum 
is 10 inches in diameter. On the same axis with the 
drum there is a wheel with 51 teeth that takes into a 
wheel with 50 teeth, on the drum-shaft. On the drum- 
shaft there is also a wheel that takes into a wheel with 34 
teeth, on the same axis with the winding-on drum. How 
many teeth should there be in the wheel on the drum-shaft 
that takes into the wheel on the same axis with the wind- 
ing-on drum ; and what should be the diameter of the 
winding-on drum, to give it a surface velocity equal to 
that of the bare spindle, when winding on the first stretch 
of yarn ? 



158 



COTTON MANTTFACTUKE. 



Diameter of the spindle- 
warl, in inclies . . 1 

Teeth in the wheel on 
the same axis with 
the drum .... 51 



.24, Diameter of the spindle, 
in inches. 

10, Diameter of the drum, 
in inches. 

50 Teeth in the wheel on 
the drum shaft that 
takes into the wheel 
on the same axis with 
the drum. 

34 Teeth in the wheel on 
the same axis with the 
winding-on drum. 



Worked out. 

.24-.08 



1 
1-3-51 



10 
50 
34-2 



50 
2 

100 
10 

1000 

.08 



{^Continued.) 



THE FKAJiTKLIN MULE. 159 

A . . . . 10)80.00 



A 2)8 

B 4)4 

1 

A. 10 X 2 20 Teeth in the wheel on the drum- 
shaft that takes into .the wheel on the same axis with the 
winding-on drum. 

B, 4 4, Diameter of the winding-on drum, in 
inches. Answer. 

The spindle is ^V ^^ ^^ i^ch in diameter, and has on a 
warl one inch in diameter, driven from a drum 10 inches 
in diameter. On the same axis with the drum there is a 
wheel with 51 teeth that takes into a wheel with 50 teeth, 
on the drum-shafb. On the drum-shaft there is a wheel 
with 20 teeth that takes into a wheel with 34 teeth, on the 
same axis with the winding-on drum. What is the sur- 
face velocity of the spindle when winding on the first 
stretch of yarn, if the winding-on drum throws off 60.0831 
inches of chain, the winding-on drum being 4 inches in 
diameter ? 



60.0831 Inches of chain 
thrown off when wind- 
ing on the first stretch 
of yarn. 



IGO 



COTTON MANUFACTURE. 



Diameter of the spindle, 
in inches 24 

Teeth in the wheel on 
the same axis with 
the winding-on drmn 34 



Teeth in the wheel on 
the drum-shaft that 
takes into the wheel 
on the same axis with 
the drmn .... 50 

Diameter of the drum, 
in inches . . . . 10 



4, Diameter of the wind- 
ing-on drum, in inches. 

20 Teeth in the wheel on 
the drum-shaft that 
takes into the wheel 
on the same axis with 
the winding-on drum. 

51 Teeth in the wheel on 
the same axis with the 
drum. 



1, Diameter of the spindle- 
warl, in inches. 



Worked out hy Cancellation. 





60.0831 


1-.24 


4-1 


•2-8.5-34 


2(04 ' 


1-50 


51-212.5-4.254 


1(0 


1 



60.0831 



Answer. 



T]ie same without Cancellation. 
Dividend . . 60.0831 x 4 x 20 x 51 
Divisor. . . .24x34x50x10 



60.0831 



Answer. 



DKESSmG-MACHINE. 



IGl 



DEESSING-MACHINE. 

A dresser is driven from an upright shaft, making 180 
revolutions per minute, by a train of three pairs of pul- 
leys and one pair of wheels ; the driving wheel has 96 
teeth, and the driving pulleys are 20, 18, and 10 inches in 
diameter, respectively. How many teeth should there be 
in the driven wheel ; and what should be the diameter of 
the driven pulleys, respectively, to drive the first driven 
shaft of the dresser 100 revolutions per minute ? 



Revolutions of the first 
di'iven shaft of the 
dresser per minute . 100 



180 Revolutions of the up- 
right shaft per min- 
ute. 

96 Teeth in the driving 
wheel. 

20, Diameter of the first 
driving pulley, in 
inches. 

18, Diameter of the second 
dri^'ing pulley, in 
inches. 

10, Diameter of the third 
driving pulley, 
inches. 



m 



162 



COTTON MANUFACTUKE. 



Worked out. 



1(00 



180 

96 

2(0 

18 

1(0 



180 
96 





1080 
1620 




17280 
2 




34560 
18 




276480 
34560 


B . . 


. 10)622080 


B . . 


. . 3)62208 



{Continued.^ 





DKESSING-lVr A CHLNB. 




c . 


. 3)20736 


A 


. . . 


. 4)6912 


A 


. . . 


. 2)1Y28 


A 




. . 2)864: 


A 




. . 4)432 




c . 


. . 3)108 




c . 


. . 3)36 




D. 


. . . 12)12 
1 



163 



A. 4x2x2x4 = 64 Teeth in the driven wheel. 

B. 10 X 3 = 30, Diameter of the first driven pulley, 
in inches. 



C. 3x3x3 



2Y, Diameter of the second driven 



pulley, in inches. 

D. 12 12, Diameter of the third driven pulley, 

in inches. 

Answer. 



From the particulars found in the preceding example, 
find the revolutions per minute of the first driven shaft of 
the dresser. 



164 



COTTON MANUFAOTUKE. 



Worked out hy Cancellation. 




18(0-6-2 


1-2-8-64 


96424 


1-3(0 


20-5 


1-9-2Y 


18-24 


142 


10 


10x5x2 


100 



TTie same without Cancellation. 

Dividend . . . 180x96x20x18x10 
Divisor .... 



Answer. 



= 100 



64x30x27x12 



Answer. 



The first driven shaft makes 100 revolutions per minute, 
and drives the centre beam by a train of 4 pairs of wheels 
and one pair of cones. The large end of the driving cone 
is 9 inches in diameter, and the driving wheels have 50, 
20, 20, and 20 teeth respectively. What should be the 
diameter of the small end of the driven cone ; and how 
many teeth should there bein the driven wheels, respect- 
ively, to give the empty beam a surface velocity of 4 yards 
per minute, the beam being 5 inches in diameter ? 

100 Revolutions per minute 
of the first driven 
shaft. 



DKESSING-MACHINE. 



165 



Inches in one yard . 



36 



Surface velocity per 
minute of tlie empty 
beam, in yards . . 4: 



9, Diameter of the large 
end of the driving 
cone, in inches. 
50 Teeth in the first driv- 
ing wheel. 
20 Teeth in the second 

driving wheel. 
20 Teeth in the tliird driv- 
ing wheel. 
20 Teeth in the fourth 
driving wheel. 
5, Diameter of the empty 
beam, in iuches. 
3.1416, Circumference. 





Worlced out. 






100 






9-3 






50 






20 






20 






20'5 




1-3-36 


5 
3.1416'.2618 




14 





166 co'rroN manufactuke. 

.2618 
5 

1.3090 
5 

6.5450 
20 

130.9000 
20 

2618.0000 
50 

130900.0000 
3 

392700.0000 
100 

E . 10)39270000.0000 



E. . . 10)3927000 



B 5)392700 



B 5)78540 

{Continued.) 



DKESSESTG-MACnmE. 167 

B 2)15708 

D 2)7854 

C 5)3927 

C 2)785.4 

C 5)392.7 

D 5)78.54 

D . . . . 3)15.708 

A 5.236)5.236 

1 

A. 5.236 5.236, Diameter of the small end of the 

driven cone, in inches. 

B. 5x5x2 == 50 Teeth in the first driven wheel. 

C. 5x2x5 == 50 Teeth in the second driven wheel. 

D. 5x3x2 = 30 Teeth in the third driven wheel. 

E. 10x10 = 100 Teeth in the beam-flange, or 
fourth driven wheel. 

Answer. 

From the particulars found in the preceding example, 
find the surface velocity of the empty beam per minute. 



1G8 



COTTON MANUFACTUKE. 



Worked out ly Ccmcellation. 




100-1 


1-2.618-5.236 


9-1 


1-50 


50-1 


1-5(0 


2(0-1 


1-3(0 


2(0 


1-100 


20-5 


1-4-36 


5-1 




3.1416-1.2-.4 


5 X 2 X .4 = 


— 4 yards. 



The sa/ine without Cancelldtion. 



Div. 



., 100 X 9 X 50 X 20 X 20 X 20 x 5 x 3.1416 
Divisor, 



5.236 X 50 X 50 x 30 X 100 x 36 



Answer. 



= 4 yards. 



Answer. 



N.B. — The surface velocity of the empty beam, as 
shown in the preceding example, is as quick as will pro- 
bably ever be required for any kind of work ; in practice 
it is found necessary to vary the velocity according to cir- 
cumstances, such as facilities for drying, fineness of yarn, 
and the progressively increasing size of the beam, which 
is done by causing the belt to traverse on the cones. 

As some kinds of work requires more wind than others, 



DKESSma-MAOHINE. 



169 



and as local circiTmstances lias more or less to do with 
making it effective, it is impossible to lay down any rule 
that will answer in all cases with respect to quantity. It 
is estimated by some mechanicians that tlie circumference 
of a fan should have a velocity of 2600 yards per minute, 
to equal a storm of wind ; the way to find which or any 
other velocity that may be required, will be found in the 
following example : 

A fan, one yard in diameter, is driven from an upright 
shaft making 180 revolutions per minute, by a train of 3 
pairs of pulleys and one pair of wheels. The driving pul- 
leys are 42, 39, and 20 inches in diameter, respectively, 
and the driving wheel has 96 teeth. What should be the 
diameter of the driven pulleys, respectively, and how 
many teeth should there be in the driven wheel, to give 
the circumference of the fan a velocity of 2600 yards per 
minute ? 



Velocity of the circum- 
ference of the fan 
per minute, in yards, 2600 



180 Revolutions per minute 
of the upright shaft. 

96 Teeth in the driving 

wheel. 
42, Diameter of the first 

driving pulley, in 

inches. 



170 



OOrrON MANUFACTUKE. 



39, Diameter of the second 
driving pulley, in 
inches. 
20, Diameter of the third 
driving pulley, in 
inches. 
1, Diameter of the fan, in 
yards. 
3.1416, Circmnference. 



Wfyrked out. 




l-13-26(00 


18(0-9 

96 

42 

39-3 

2(0 

1 

3.1416 






96 




9 




864 




42 




1728 




3456 


{Continued 


•) 





DKESSING-MACHmE. 171 

36288 
3 

108864 
2 

2in28 
3.1416 

1306368 

217Y28 
870912 
217728 
653184 

A . . . . . 12)684014.2848 

A 7)57001.1904 

B 6)8143.0272 

B 6)1357.1712 

G 8)226.1952 

C .... 4)28.2744 

D . . . 7.0686)7.0686 

1 



172 



COITON AIANUFACTURE. 



= 84 Teeth in the driven wheel; 
36, Diameter of the first di'iven pulley, 

32, Diameter of the second driven pulley, 

= Y.0686, Diameter of the third driven 



A. 12x7 = 

B. 6xQ = 
in inches. 

C. 8x1 = 
in inches. 

D. 7.0686 
pulley, or pulley on the same axis with the fan, in inches. 

Answer. 

From the particulars found in the preceding example, 
find the velocity per minute of the circmnference of the 
fan. 

Worked out hy Cancellation. 



1-7-84 
1-6-36 
14-32 

l-2.^5-7.0686 



180-8040 

96-8 

12-6-1 

39-6.5 

20-5 

1 

3.1116-1 



Dividend, 
Divisor, 



10 X 8 X 5 X 6.5 = 2600 yards. 

TTie smne without Ccmcellation. 
180 X 96 X 42 X 39 X 20 X 3.1416_ 
81x36x32x7.0686 



Answer. 

2600 yards. 
Answer. 



DRESSING-MACHINE, 



173 



In practice it is found, tliat on account of shrinkage in 
weaving a certain kind of cloth, that it takes 1,04 Y2 yards 
of warp to make one yard of cloth. The warp is mea- 
sured by the neck-roller, on the end of which there is a 
worm that takes into a wheel with 100 teeth, and every 
time the wheel makes a revolution it causes a mark to be 
made on the warp ; this mark indicates where to cut the 
cloth into lengths called cuts (hence the term cut-mark). 
"What should be the diameter of the neck-roller, to mark 
the warp into lengths requisite for weaving cuts of cloth 
42 yards long ? 



Teeth in the wheel that 
takes into the worm. 100 

Katio of circumference 
to diameter . . 3.14:16 



42, Length of a cut of cloth, 

in yards. 
36 Inches in one yard. 



1.04Y2, Length of warp re- 
quired for one yard of 
cloth, in yards. 



Worked out hy Cancellation. 
424.2-,42 
36-12 
1-10400 

{Continued.) 



1T4 COTTON MANUFACTUKE. 

1-3-3.1416 

l.(M724 



12 X .42 5.04 inches. 

Answer. 



The same without Ca/ncellation. 
Dividend 42x36x1.0472 



6.04 



Divisor 100x3.1416 

Answer. 

From tlie particulars found in the preceding example, 
find the number of yards in a cut of cloth. 

Worked out hy CcmcellaUon. 



1-12-36 



1-1.04Y2 



5.04-.42 

3.1416-3-1 

100 



100 X. 42 = 42 



Answer. 



The same witJwut Ca/ncellation. 
Dividend 5.04x3.1416x100 



:42 



Divisor 36x1.0472 

Answer. 



POWEK-LOOM. 



175 



POWEK-LOOM. 



A loom is driven from an upright sliaft making 180 
revolutions per minute, by a train of two pairs of pulleys 
and one pair of wheels. The driving pulleys are 17^, and 
8 inches in diameter, and the driving wheel has 96 teeth. 
What should be the diameter of the driven pulleys, 
respectively, and how many teeth should there be in the 
driven wheel, to drive the loom 140 picks per minute ? 



Picks per minute of the 
loom 140 



180 Revolutions per minute 
of the upright shaft. 
96 Teeth in the driving 
wheel. 
17.5, Diameter of the first 



driving 



pulley. 



m 



inches. 
8, Diameter of the second 
driving pulley, in 
inches. 



Worked out. 



1-744(0 



18(0-9 

96 

17.5-2.5 



(^Continued.) 



176 COTTON MANtlFAOTUEE, 

96 

9 

864 
8 

6912 
2.5 

34560 
13824 

A 8)17280.0 

A 8)2160 

C 12)270 

B 22.5)22.5 

1 

A. 8x8 64 Teetli in the driven wheel. 

B. 22.5 22.5, Diameter of the first driven pulley, 

in inches. 

C. 12 = 12, Diameter of the second driven pulley 
on the crank-shaft of the loom, in inches. 

Answer. 

From the particulars found in the preceding example, 
find how many picks per minute the loom will make. 



POWEE-LOOM. 



177 



Worked out hy Cancellation. 
180-200 



1-8-64: 

1-.94.5-22.5 

1-12 



96-124 
17.5-3.5-.7 

84 



200 X .7 



MO 



Answer. 



Ths same without Cancellation. 

Dividend .... 180x96x17.5x8 . 
Divisor 64x22.5x12 



140 



Answer. 



The rateliet wheel of the take-up motion has 80 teeth, 
and takes up one tooth every two picks, and the emery- 
roller wheel has 90 teeth. How many teeth should there 
be in the wheel that takes into the emery-roller wheel ; 
and what should be the circumference of the emery-roller 
to produce cloth with 72 picks per inch ? 



80 Teeth in the ratchet- 
wheel. 
2, Takes up one tooth every 
two picks. 

90 Teeth in the emery-roll- 
er wheel. 

8* 



178 



COTTON MAJifTIFACTTIRB. 



Picks per ] 


nch in 


the 








cloth . . 


. . . 


. 72 












Worked out. 












80-10 












2 




_ 








90-10 










l'9-72 
















10 












10 












100 












2 






A . 


. . . 


. . . 


8)200 






A . 


• • • 


• • • 


2)25 






B 


. . . 


. . 12 


.5)12.5 





A. 8x2 



16 Teeth in the wheel that takes into 



the emery-roller wheel. 

J3. 12.5 = 12.5, Circumference of the emery-roller, 

in inches. 

Answer. 



POWEK-LOOM. 



179 



From tlie particulars found in the preceding example, 
find the picks per inch in the cloth. 



Worked out hy Cancellation. 




80-54 




24 


146 


9048 


1-.5-2.6-12.5 




18x4. 


n 



Answer. 



The same without Cancellation. 
Dividend 80x2x90 



= 72 



Divisor ........ 12.5 x 16 

Answer. 

From the particulars found in the preceding example, 
find the number of teeth in the ratchet wheel. 



Worlcsd out hy Cancellation. 



140-90 



1-2 



16 
12.54.25 

72-84 



16x4x1.25 



80 



Answer. 



180 COTTON MAKUFACTUKE. 

Tlie sa/me without Cancellation. 
Dividend 16x12.5x72 



80 



Divisor ., 90x2 

Answer. 

From the particulars found in the preceding example, 
find how many picks the loom makes while the ratchet- 
wheel moves one tooth. 

Worked out hy Cancellation. 



140-90 



1-5-80 



164 
12.5-2.5 

72-8-.8 



2.5 X. 8 



Answer. 



TTie same without Cancellation. 
Dividend 16x12.5x72 



2 



Divisor 90x80 

Answer. 

From the particulars found in the preceding example, 
find the number of teeth in the emery-roller wheel. 



POWEK-LOOM. 



181 



Worked out hy Cancellation. 


' 


16-.1 




12.5-2.5 




72-36 


1-5-80 




1-2 




36x2.5 


90 



Answer. 



The same without Cancellation. 

Dividend 16x12.5x72 . 

Divisor 



90 



80x2 



Answer. 



From the particulars found in the preceding example, 
find the number of teeth in the wheel that takes into the 
emery-roller wheel. 



Worked out hy Ca/ncellation. 
90-18-1 



1-.5-2.5-12.5 
1-2-36-72 



2-1 

80-40-8-16 



16 



Answer. 



182 COTTON MANUFACTUEE. 

The same without Ccmeellation. 
Dividend 90 x 2 x 80 



16 



Divisor 12.5x72 

Answer. 

From the particulars found in the preceding example, 
find the circumference of the emery-roller. 



Worhed out hy Cancellation. 


1-16 


9040 




24 




80-54.25 


14-8-Y2 





10 X 1.25 = 12.5 inches. 

Answer. 



The sa/me without Cancellation. 
Dividend 90x2x80 



12.5 



Divisor 16x72 

Answer. 

If the circumference of the emery-roller is 12|^ inches, 
what will be its diameter ? 

12.5 ^ 3.1416 = 3.9788+ inches. 

Answer. 

If a change-wheel with 16 teeth puts in 72 picks per 
inch, how many picks per inch will a change-wheel with 
18 teeth put in ? 



POWEK-LOOM. 



183 



Worked out hy Cancellation. 

724 



148 



16 



16x4 



64 



Answer. 



The same without Cancellation. 

Dividend Y2xl6 . 

Divisor 18 



64 



Answer. 

The taking-iip ratchet-wheel has 96 teeth, and on the 
same axis there is a wheel that takes into a wheel with 90 
teeth, on the same axis with the emery-roller. How many- 
teeth are tliere in the wheel on the same axis with the 
ratchet-wheel ; and what is the circumference of the 
emery-roller, if the loom is putting in 100 picks per inch, 
and taking up one tooth every 2 picks ? 



Picks per inch in the 
cloth 100 



96 Teeth in the ratchet- 
wheel. 

90 Teeth in the wheel on 
the same axis with the 
emery-roller. 

2 Picks put in while the 
ratchet-wheel takes up 
one tooth. 



184 



COTTON MANUTACTUKE. 



Worked out. 




96 






9(0 


-.9 


140(0 


2' 








96 






.9 






86.4 






2 


A . . . 


• • 


6)172.8 


A . . . 


• • 


3)34.56 


B . . 


11. 


52)11.52 



A. 5x3 



15 Teeth in the wheel on the same axis 



with the ratchet-wheel. 

B. 11.52 = 11.52, Circumference of the emery- 



roller, in inches. 



Answer. 



From the particulars found in the preceding example, 
find the picks per inch in the cloth. 



POWER-LOOM. 185 



Worked out hy 


Cancellation. 




2 




96400 


1-345 


90-7.54.5-.5 


1-.9641.52 




100 X 2 X . 


5 100 



TJie same without Cancellation. 
Dividend 2x96x90 



Answer. 



= 100 



Divisor 15 X 11,52 

Answer. 

The taking-iip ratchet-wheel containing 96 teeth takes 
up one tooth every 2 picks. On the same axis with the 
taking-up ratchet-wheel there is a wheel with 15 teeth that 
takes into a wheel on the same axis with the emery-roller 
containing 90 teeth. The diameter of the emery-roller is 
to that of the full beam as one to 3. The beam-flange 
containing 108 teeth takes into a wheel on a horizontal 
shaft. On the horizontal shaft there is also a wheel with 
14 teeth that takes into a worm. On the same axis with 
the worm there is a wheel with 28 teeth that takes into a 
wheel on the same axis with the let-oif ratchet-wheel ; the 
latter wheel contains 120 teeth. How many teeth should 
there be in the wheel that takes into the beam-flange, and 



186 



COTTON MANUFACTURE, 



the wheel on the same axis with the let-off ratchet-wheel, 
if the latter wheel lets off one tooth per pick while weav- 
ing the first lap of a full beam, making no allowance for 
shrinkage in weaving ? 



Teeth in the taking-up 
ratchet-wheel ... 96 



Teeth in the wheel on 
the same axis with 
the emery-roller . . 90 

Relative diameter of the 
full beam .... 3 



.5, The taking-up ratchet- 
wheel takes up one 
tooth every 2 picks, 
which is equal to one 
half tooth per pick. 

15 Teeth in the wheel on 
the same axis with 
the taking-up ratchet 
wheel. 
1, Relative diameter of 
the emery-roller. 
108 Teeth in the beam- 
flange. 

14 Teeth in the wheel that 
takes into the worm. 

28 Teeth in the wheel that 
takes into the wheel 
on the same axis with 
the let-off ratchet- 
wheel. 
120 Teeth in the let-off 
ratchet-wheel. 



POWEK-LOOM. 


187 


Worked out. 




1-8-96 


.5 




1-9(0 


15-5 




1-3 


1 

108-9-1 

14 

28 
12(0-1.5 






28 




1.5 




140 




28 




42.0 




14 




1680 




420 




588.0 




5 


( 


3940.0 




.5 


{.Continued^ 







188 



COTTON MANUFACTURE. 

A .... . 10)14Y0.00 

B 7)147 

B 7)21 

A 3)3 



A. 10x3 



30 Teeth in tlie wheel that takes into 



the beam-flange. 

B. 7x7 49 Teeth in the wheel on the same axis 

with the let-off ratchet-wheel. 

Answer. 

From the particulars found in the preceding example, 
find how many teeth the let-off ratchet-wheel will move 
while the loom makes one pick. 

Worked out by Cam^ceTlation. 



1-2-8-96 

1-9(0 

1-3 

1-345-30 

1-749 
2x.5 



12(0-4-1 

.5 

15-5-1 

108-9-1 
14-2-1 

28-4-2 



Answer. 



WEIGHmG YAUN, SLIVEE, ETC. 189 



The same without Ca/nceUation. 
Dividend . . 120 x. 5 x 15 x 108 x 14x28 



Divisor. . . 96x90x3x30x49 



WEIGHISTG TAEF, SLIVER, ETC. 



= 1. 



Answer. 




Correct instruments for weighing 
the sliver, roving, and yarn, in the 
various branches of carding and 
spinning, are of snch vast import- 
ance in the manufactm^e of cotton 

that the author has taken the hberty to mention a very 
excellent kind of scales, made by J. R. Brown & Sharpe, 
Providence, E.. I. They are intended for very delicate 
weighing, the tenth of a grain being easily estimated by 
them. Their general construction is so simple that the 
cut will show it without a description. The length of the 
beam is about eight inches, and the long arm, which has a 
small weight sliding upon it, is divided into a hundred 
parts ; these divisions indicate grains, and are numbered so 
as to be easily read. On the end of the long arm ^f the 
beam is a small pan, or hook, on which other weights 
are placed when more than 100 grains are required to be 
weighed. The extra weights are numbered 100, 200, 400, 
and 800, so that any number, from one to 1600 grains, 
can be weighed by them. 

As will be seen, the following tables are all made with 



190 COTTON MANUFACTURE. 

a view to using some such scales as the above, but will 
answer equally well for any scales by which the weight in 
grains can be ascertained. 

The following table for weighing with troy weight, and 
reckoning by avoirdupois weight, will be found useful to 
those who use ounces, pennyweights, and grains, with the 
" beam and pans " scales : 

24 grains equal one pennyweight. 

18 pennyweights 5|- grains, troy, equal one ounce 
avoirdupois. 

16 ounces equal one pound. 

The home-made weights too commonly used, made from 
bits of tin, wire, lead, or other small pieces of metal, can- 
not, as a general thing, be depended upon as being very 
correct, not because they cannot be made a definite weight, 
but rather because few have the means of making them 
so. Suppose that for want of sufficiently delicate tools in 
adjusting a weight of 175 grains, we should happen to 
make it 1T6 grains ; the difference would be but one 
grain, yet the consequence would be considerable. 1Y5 
grains weight of l^o. 40 cotton yarn, is 840 yards in 
length, and 1Y6 grains weight of the same is 844.8 yards 
in length, a difference of 4.8 yards per hank, or 192 yards 
per pound. Yery true, yarn can be made as regular in 
size by using such weights ; but as to the accuracy of the 
size, it cannot be called better than a mere guess. 



PART II. 

CAJBDING. 
YARN, ROVING, AND SLIVEE TABLES. 

54 inches == 1 thread. 
4320 inches = 80 = 1 lea. 
30240 inches = 560 = 7 = 1 hank, or 840 yards. 

Counts of yarn and hank-roving signify the number of 
hanks in one pound. 

Whatever number of yards are weighed, multiply them 
by the number of grains in one pound avoirdupois, for a 
dividend, and their weight in grains by the number of 
yards in one hank for a divisor, and the quotient will be 
the number. 

One hank contains 840 yards, and one pound avoirdu- 
pois contains 14 ozs. 11 dwts. 16 grains, troy, or YOOO 
grains. Hence, the yards in one hank are to the grains 
in one pound as 840 is to 7000, or 12 to 100. 

IST.B. — See tables on page 281. 

Mvample. 
If 50400 yards weigh one pound, what is the number ? 



192 COTTON MANUFACTUKE. 



Worked out hy Cancellation. 



1-7(000 
1-12 



5040(0-720-60 
1(00 



60 

Answer. 



TTie same without Cancellation. 

Dividend 50100 x 100 _^^ 

Divisor 7000x12 

Answer. 



How many yards are there in one pound of No. 60 
yam? 

WorJced out hy Cancellation. 
70(00 



1(00 



60 
12 



70x60x12.^=50400 

Answer. 

The same without Cancellation. 
Dividend 7000x60x12 



50400 



Divisor 100 

Answer. 



CAKDING. 193 

K.B. — The same result will be found by multiplying 
the nmnber of yards in one hank by the number. 

Exarrvple. 
840x60 = 50400. 

Answer. 

What is the weight of 50400 yards of ISTo. 60 ? 

WorTced out hy CanceUation. 
50400-8400-700 



1-6(0 
142 



10(0 



TOO X 10 TOOO grains, or one pound avoirdupois. 

Answer, 

The same without Cancellation. 
Dividend 50400x100 



TOOO • 
Divisor ....... 60x12 

Answer. 

N.B. — It is by the above rule that all the compendious 
tables are made, 

Mcamples explam,atory of the sli/ver, roving, a/nd yarn 

tahles. 

What is the weight of 6 yards of Ko. .025 sliver ? 

9 



194 

ITo. of the sliver 



COTTON MANUFACTURE. 



.025 



^ of 840 12 



6, Length of sliver, in 



yards. 



100 -Jg- of YOOO. 



Worked out l)y Cancellation. 



1-.025 
1-2-12 



64 
100-50-2000 



2000 grains. 



The same without Cancellation 
Dividend 6x100 



Answer. 



Divisor 025 x 12 



= 2000 grains. 



Answer. 



If 6 yards of sliver weighs 2000 grains, what is the 
number ? 

Worked out hy Cancellation. 



1-2000 
1-242 



64 
100-50-.025 



.025 



Answer. 



The same without Cancellation. 
Dividend 6x100 



.= .025 



Divisor 2000 x 12 



Answer. 



CARDING. 195 

How many yards of 'No. ,025 sliver will it take to weigh 
2000 grains ? 

Worked out hy GanceUation. 
20(00 



1(00 



.025 
12 



20 X 12 X .025 = 6 

Answer. 



The sa/me without Gam,ceUation. 
Dividend 2000 x. 025x12 



= 6 



Divisor 100 

Answer. 

What is the weight of 12 yards of a four-hank roving % 
Worked out hy GanGellation. 



1-4: 

142 



12-1 
100-25 



25 grains. Answer. 

The same without GanceUation. 

Dividend 1^x100= 25 grains. 

Divisor 4x12 

Answer. 



196 COTTON MANUFACTURE. 

I 12 yards of roving weigh 25 grains, what is the 
number ? 

Worked out hy Cancellation. 



1-25 
142 



12-1 
1004 



4 Answer. 

The same without Cancellation. 
Dividend 12x100 , 



Divisor 25 x 12 

Answer. 

How many yards of a four-hank roving will it take to 
weigh 25 grains ? 

Worked out hy Ca/ncellation. 
254 



14400 



44 
12 



12 Answer. 



The sa/me without Cancellation. 
Dividend 25x4x12 



12 



Divisor 100 

Answer. 



CAKDING. 19Y 

What is the weight of 840 yards or one hank of ISTo. 
40 yarn ? 

Worked out l>y Cancellation. 



14(0 
142 



84(0-7 
100-25 



25 X Y 175 grains. 



Answer. 



The sa/me without Ga/ncellation. 

Dividend 840x100 ^^^ 

= 175 grains. 

Divisor 40x12 

Answer. 

If 840 yards of yarn weigh 175 grains, what is the 
number ? 

Worked out lyy Cam^cellal/ion. 



1-7-175 
1-12 



840-70-10 
100-4 



10 X 4 = 40 Answer. 



The sa/me without Ca/ncellation. 
Dividend 840 x 100 



= 40 



Divisor 175 x 12 

Answer. 



198 



COTTON MANUFACTURE. 



How many yards of N"©. 40 will it take to weigh 175 
grains ? 

W(yrked out hy Ocmcellation. 
175 
4(0-.4 



140(0 



12 



175xl2x.4 



840 



Answer. 



The scmie witJwut CoMcellation. 

Dividend 175 x 40x12 

Divisor 



= 840 



100 



Answer. 



If 30 ounces of cotton is spread 48 inches in length, 
what proportion of a hank is it ? 



Weight of a spread, in 

ounces 30 

Inches in one yard . . 36 

Yards in one hank . . .840 



16 Ounces in one pound. 

48, Length of a spread, in 
inches. 



Worked out hy Cancellation. 



30 
9-36 

70-840 



16 
4844 



16 -T- 70 X 30 X 9 = 0.00084656^^ Answer. 



CAKDING. 



199 



The samie without Ga/rwellation 

Dividend . . . 16x48 

Divisor . . . 30x36x840 



0.00084666^^ 



Answer. 



If 30 ounces of cotton is spread on 48 inches of lattice, 
and the doublings are 3 at the finisher-lapper, 80 at the 
breaker-card railway, 8 at the finisher-card railway, 2 at 
the first head of drawing, 4 at the second head of draw- 
ing, 2 at the third head of drawing, and 2 at the fine fly- 
frame, what should be the draught at the mule, the fine 
fly-frame, the coarse fly-franie, the third head of drawing, 
the second head of drawing, the first head of drawing, the 
railway head, the finisher-cards, the breaker-cards, the 
finisher-lapper, and the breaker-lapper, to produce IS^o. 40, 
making an allowance of 14 per cent, for loss in working ? 



Ounces in one pound . 16 

Length of a spread, in 
inches 48 



Cent 



100 



30, Weight of a spread, in 

ounces. 
36 Inches in one yard. 

840 Yards in one hank. 
40 l!^o. produced. 
86, Cent less 14. 
3, Doubling at the finisher- 
lapper. 



200 



COTTON MANtTFACTUEE. 



80, Doubling at the break- 
er-card railway. 

8, Doubling at the finish- 
er-card railway. 

2, Doubling at the fii'st 
head of drawing. 

4, Doubling at the second 
head of drawing. 

2, Doubling at the third 
head of drawing. 

2, Doubling at the fine 
fly-jframe. 



1(00 



Worked out. 

1-2-16 3(0 
1448 36 

84(0-7 

40 

86 

3 

80 

84 

24 

4-1 

2 

2 



{Continued^ 



CAKDING. 201 

36 
3 

108 
7 

756 
40 

30240 
86 

181440 
241920 

2600640 
3 

7801920 
80 

624153600 
2 

1248307200 
2 

G- . . . . 2)2496614400 

(Continued.) 
9* 



202 



C 



COTTON MA 

D . . . 


JSiM 


FAC 


TIJ] 


BE. 

2)1248307200 


D . . . 


2)624153600 


E . . . . 

E . . . 


2)312076800 
2)156038400 


F . . . 




2)78019200 


F . . . 
H . 


2)39009600 
2)19504800 


H . 


2)9752400 


H 


2)4876200 


H 


. 2)2438100 
2)1219050 


1 
I 


.• . 2)609525 
. 2)304762.5 


1 


. 2)152381.25 


1 


. 2)76190.625 


I 

{Continued.') 




5)38095.3125 



CAKDING. 203 

C 8)Y619.0625 

A 3)2539.6875 

A 3)846.5625 

J . . . 3)282.1875 
H . . . . . 6)94.0625 

B 7)18.8125 

K . 2.6875)2.6875 

1 

A. 3x3 = 9, Drauglit at the mule. 

B. 7 = 7, Draught at the fine fly-frame. 

C. 3x2 = 6, Draught at the coarse fly-frame. 

D. 2x2 == 4, Draught at the third head of drawing. 

E. 2x2 ==: 4, Draught at the second head of drawing. 
r. 2x2 = 4, Draught at the first head of drawing. 
G. 2 = 2, Draught at the railway head. 

H. 5x2x2x2x2 80, Draught at the finisher- 
cards. 

I. 5x2x2x2x2 80, Draught at the breaker- 
cards. 

J. 3 = 3, Draught at the finisher-la]3per. 

K 2.6875 2.6875, Draught at the breaker-lapper. 

Answer. 



204 



COTTON MANUFACTUKE. 



From the particulars found in the preceding example, 
find the number produced. 

Worked out hy Cancellation. 



1-3(0 


16-2-1 


1-9-36 


484-1 


l-7-84(0 




1-2.687540.7543-86 


1(00 




2.6875-1 


1-3 


3-1 




80-1 


1-80 


80-40 


1-8 


2-1 


1-2 


4-1 


14 


4-1 


1-2 


4-1 




6-24 


1-2 


7-1 




94 



40 



Answer. 



The same without Cancellation. 
Dividend, 16 x 48 x 100 x 2.6875 x3x80x80x2x4 

X4x4x6x7x9 . 

Divisor, 30 x 36 x 840 x 86 x 3 x 80 x 8 x 2 x 4 x 2 
x2 

Answer. 



40 



CAEDING. 



205 



From the particulars found in the preceding example, 
find the weight of a spread. 



Worked out hy CcmcellaUon. 




16-2-1 Ounces in one pound. 


1-9-36 


4844 


l-7-84(0 




1-2.6875-10.Y543-86 


10(0-5 




2.68754 


1-3 


34 




804 


1-80 


80-24 


1-8 


24 


1-2 


4-1 


14 


4-1 


1-2 


4-1 




6 


1-2 


7-1 




94 


140 




6x5 


30 ounces. Answer. 



The same without Ccmcellation. 
Dividend, 16 x 48 x 100 x 2.6875 x3x80x80x2x4 

X4x4x6x7x9 

Divisor, 



:30 



36x840x86x3x80x8x2x4x2x2 
x 40 Answer. 



20G 



COTTON MANUFACTURE. 



From the particulars found in the preceding example, 
find the length of a spread. 



Worked out hy Cancellation. 




364 Inches in one yard. 


1-246 


3(04 




84(042 


1(00 


86-21.5-5.375-2.68Y64 


1-2.68Y5 




1-3 


34 


1-80 




1-2-80 


80-] 


1-2 


84 


14 


24 


14 


44 


14 


24 


1-3-6 




1-Y 


24 


1-9 






404 


12 X 4 


48 inches. Answer. 



The same without Cancellation. 
Dividend, 36 x 30 x 840 x 86 x 3 x 80 x 8 x 2 x 4 x 2 



Divisor, 



x2x40 



16 X 100 X 2.68Y5 x3x80x80x2x4 
x4x4x6x7x9 Answer. 



-=48 



CAJBDING. 



20Y 



From the particulars found in the preceding example, 
find the decimal of a hank of a spread. 



Worked out hy Ccmcellation. 




4(0 


9 




7 


24 


3-6 




14 


24 


1-4: 


44 


14 


24 


1-2 


84 


540-80 


804 


1-80 




1-3 


34 


1-2.68T5 




540(0 


86-21.5-5.375-2.68754 


4-^9x7x3x5x5 = 0.00084656^ 




Answer. 



The sarnie without Ca/ncellation. 



Div. 40x2x2x4x2x8x80x3x68 . 
Divis. 9x7x6x4x4x4x2x80x80 
x 3 X 2.6875 x 100 



0.00084656^ 



Answer. 



208 



COTTON MANUFACTHEE. 



From the particulars found in the preceding example, 
find what the number would be if there was no loss in 
working. 



Worked out hy Ccmcellation. 





1-5-30 


16-2-1 




14-36 


484-2 




l-7-84(0 


2.6875-.53T5 




1-3 


34 


« 




804 




1-80 


8(0 




1-8 


2-1 




1-2 


4-1 




14 


4-1 




1-2 


4 
64 




1-2 


7-1 
9-1 




.53T5 X 2 X 8 


X 4 34.4 Answer. 



Div. 



Divis. 



The same without Ccmcellation. 

16 X 48 X 2.6875 x3x80x80x2x4x4x4 
x6x7x9 



34.4 



30x36x840x3x80x8x2x4x2x2 

Answer. 



CAEDING. 209 

K.B. — The particulars found in the fourteen following 
examples, are taken from the above. 

From the particulars found in the preceding example, 
find the decimal of a hank, produced at the breaker-lap- 
per, commencing at the length and weight spread on the 
lattice, making no allowance for loss in working. 



Worked out hy CcmcellaUon. 



30 

9-36 

TO-840 



16 
484-1 

2.68Y5 



2.6875 X 16 -^ 70 X 9 X 30 = 0.00227 3^ 

Answer. 



The sa/me without Ccmcellation. 

Dividend. . . 16 x 48x2.6875 ^ ^ q^^^;^ ^^ 
Divisor ... 30x36x840 ' ^^ 

Answer. 

Find the decimal of a hank produced at the breaker- 
lapper, commencing at the number produced, making no 
allowance for loss in working. 



210 



COITON MANUFACTURE. 



I) 



IV. 



Worked out hy Cancellation. 







34.48.6-.86 






9 








7 


24 






6 








1-24 


2-1 






14 


41 






14 


2-1 






1-2 


8-1 






140-80 


804 






1-80 








1-3 


3-1 




.86 


-^9x7x6^ 


0.009,^,7 ,Vg- 


Answer. 



The sa/me without Ga/ncellation 
34.4 X2x2x4x2x8x80x3 



Divisor, 9x7x6x4x4x4x2x80x80x3 



= 0.00227^^ 



Answer. 



Find the decimal of a hank produced at the breaker- 
cards, commencing at the length and weight spread on 
the lattice, making no allowance for loss in working. 

Worked out hy CoMoellation. 



1-5-30 
9-36 



16-44 

48-8 



{Conti/nued^ 



CAEDING. 



211 



21-84(0 



1-3 



2.68Y5-.63T5 

34 

8(0 



.5375 x8x8-T-21x9 = 0.182 -jf 

The sa/me without CcmcellaUon. 
Dividend, 16 x48 x2.68Y5 x3 x80 
Divisor, 30 x 36 x 840 x 3 



Answer. 



0.182^ 
Answer. 



Find the decimal of a hank produced at the breaker- 
cards, commencing at the number produced, making no 
allowance for loss in working. 



Worked out hy CcmcellaUon. 




34.4 


9 




7 


24 


3-6 




1-4 


24 


1-4 


44 


1-2-4 


24 


1-2 


8-24 


1-80 


804 



34.4 -^9x7x3 = 0.182 ^f^ Answer. 



212 



COTTON MANUFACTUBE. 



The same without Ca/ncellation. 
Dividend, . . 34.4:x2x2x4x2x8x80 _ 
Divisor . . . 9x7x6x4x4x4x2x80 



0.182 -rf, 



Answer. 



Find the decimal of a hank produced at the railway- 
head, commencing at the length and weight spread on the 
lattice, making no allowance for loss in working. 

Worked out J)y CancellaUon. 



3-6-30 


16 


9-36 


484-1 


7-84(0 




- 


2.6876-.5375 


1-3 


34 




80-1 


1-80 


8(04 


1-8 


24 



.5375 X 16 ^3x9x7 = 0.0455 -A 



TST 



Answer. 



The sa/me without Cancellation. 

Dividend, 16 x 48 x 2.6875 x 3 x 80 x 80 x 2 _ ^ ^^gg - 
Divisor, 30x36x840x3x80x8 ~ 

Answer. 



CAHDING. 



213 



Find the decimal of a liank produced at the railway- 
head, commencing at the number produced, making no 
allowance for loss in working. 

Worked out hy Cancellation. 
34.4-8.6 



9 




Y 


2-1 


3-6 




•2-4 


24 


1-4 


44 


1-4 


24 



8.6 -^ 9 X Y X 3 = 0.0455 ^ 

The same without Cancellation. 
Dividend . . 34.4 x2x2x4x2 
Divisor . . 



Answer. 



9xYx6x4x4x4 



= 0.0455 y|. 



Answer. 



Find the decnnal of a hank produced at the first head 
of drawing, commencing at the length and weight spread 
on the lattice, making no allowance for loss in working. 

WorTced out hy Co/ticellation. 



16 
48-44 



3-6-30 
9-36 
7-84(0 
{Continued.) 



214 



COrrON MAJSfUFACTUEE. 





2.6875-.53T5 


1-3 


34 




8(0-1 


1-80 


804 


1-8 


24 


1-2 


4-2 



.53Y5 xl6x2^9x7x3 = O-OOl^^ 



Answer. 



The sarnie without Cancellation. 
Div. 16 X 48 X 2.6875 x3x80x80x2x4 
Divisor, 30 x 36 x 840 x 3 x 80 x 8 x 2 



=: 0.091 -rfj 



Answer. 



Find the decimal of a hank produced at the first head 
of drawing, commencing at the number produced, making 
no allowance for loss in working;. 



Worked out hi 


( CoAicellation. 




34.4-8.6 


9 




Y 


2 


3-6 




1-4 


2-1 


1-4 


4-1 



8.6x2^9x7x3 = 0.09ia 



T87 



Answer. 



CARDING. 



215 



The same without Cancellation. 
Dividend .... 34.4x2x2x4 , 
Divisor . . . . 9xTx6x4x4 



0.091t| 



TST 



Answer. 



Find the decimal of a liank produced at tlie third head 
of drawing, commencing at the length and weight spread 
on the lattice, making no allowance for loss in working. 

Worked out hy GomxieUajtion. 



3'6-30 


16 


9-36 


48-4 


T-84(0 






2.68Y5-.53Y5 


1-3 


3-1 




8(0-1 


1-80 


804 


1-8 


24 


1-2 


44 


1-4 


44 


1-2 


4-24 



.53Y5 xl6x4-T-9xYx3 = 0.182^ 



Answer. 



The same without Cancellation. 
Dividend, 16 x 48 x 2.6875 x3x80x80x2x4 

x4x4 

Divisor, 30 x 36 x 840 x 3 x 80 x 8 x 2 x 4 x 2 



= 0.182^ 



Answer. 



216 



COTTON MANUFACTURE. 



Find tlie decimal of a hank produced at the third head 
of drawing, commencing at the number produced, making 
no allowance for loss in working. 

Worked out hy CcmcellaUon. 
34.4 



9 

Y 
3-6 



2-1 



34.4 -=- 9 X 7 X 3 r= 0.182t|^ 



Answer. 



The same without Cancellation. 
Dividend 34.4x2 



9x7x6 



= 0.182^ 



Answer. 



Find the hank-roving produced at the coarse fly-frame, 
commencing at the length and weight spread on the lat- 
tice, making no allowance for loss in working. 



Worhed out hy Ga/ncellation. 



1-5-30 


16 


9-36 


48-4 


7-84(0 






2.6875-.5375 


{Conti 


nued.) 



CAKDING. 



217 



1-3 

1-80 
1-8 
1-2 
14 
1-2 



34 

8(04 

804 

2 

44 

44 

4-24 

64 



Answer. 



.5375 xl6x4x2-^9x7 = 1.092^ 

The same without Cancellation. 

Div. 16 X 48 X 2.6875 x3x80x80x2x4 

x4x4x6 . 

Divisor, 30x36x840x3x80x8x2x4x2 



1.092^ 



Answer. 



Find the hank-roving produced at the coarse fly-frame, 
commencing at the number produced, making no allow- 



ance for loss in working. 



34.4 



34.4 X 2 H- 9 X 7 = 1.092^ 
10 



Answer. 



218 



COITON MANUFACTUKE. 



Find the hank-roving produced at the fine fly-frame, 
commencing at the length and weight spread on the lat- 
tice, making no allowance for loss in working. 



Worked out hy Ocmcellation. 



1-5-30 


16 


9-36 


484 


142-84(0 






2.68Y5-.5375 


1-3 


34 




8(04 


1-80 


804 


1-8 


24 


1-2 


44 


14 


44 


1-2 


4-24 




64 


1-2 


74 



.53Y5x4xl6-^9 = 3.8| 



Answer. 



The samfie without Cancellation. 

Div. 16 X 48 X 2.6875 x3x80x80x2x4x4x4 
x6x7 



3.84 



Divisor, 30x36x840x3x80x8x2x4x2x2 

Answer. 



CAKDING, 



219 



Find the hank-roving produced at the fine fly-frame, 
commencing at the number produced, making no allow- 



ance for loss in working. 



344 



34.4 ^ 9 = 3.8| 



Answer. 



From the length and weight spread on the lattice, the 
doubling, and the particulars given, to find the draught at 
each and every machine from the lapper to the mule. 
Find the nimaber produced, making an allowance of 14 
per cent, for loss in working. 

Worked out hy Cancellation. 



1-3(0 


16-24 


1-9-36 


48-4-1 


l-7-84(0 




•2.68Y5-10.Y543-86 


1(00 


Single. 


Breaker-Lapper. 


14 


6.98Y5-2.68754 


1-9 


30-3-1 


14545 


100-1 


1-2-32 


T2-8-2-1 


1-32 


32-1 


1400 


154 


{Conti 


nued.) 



220 



COrrON MAJSrUFACTUKE. 





1-2.6-26 


164 


Doublings 


. . . 1-3 


Finislier-Lapper 




14 


7-1 , 




1-9 


3(0-1 




1-2-642 


Y8-3-1 




1-2-32 


8(0-4-2-1 




1-2-32 


36-4-1 




1(00 


164 




1-26 


16-1 




Single. 


Breaker Cards. 




14.54.5 


1(0 




1(0 


33-1 




143 


6(0-3-1 




1-33 


5(0-1 




1-20 


80-40 




1-24 


15-1(0 




1-840 


9143-1 




1-7(0 


16-2-1 




1(00 


20-1 


Doubling . . 


. . 1-80 


Finisher Cards. 




1-1.5-4.5 


1(0 




1(0 


334 




143 


6(0-3-1 




1-33 


5(04 




1-20 


80-1 




1-24 
{Conti 


154(0 
',nued.) 



CARDING. 



221 



Doubling 



Doubling 



Doubling 



Doubling 



1-840 

1-7(0 

1(00 

. . 1-8 

1 

1-80 

1-4-100 

1-4-18 

1-3 

1-.5-1.5-51 

. . 1-2 

1 

1-6(0 

1-3-36 

1-27 

. . 1-4 

1 

1-6(0 

1-3-36 

1-27 

. . 1-2' 

1 

1-6(0 

1-3-36 

1-27 

Single. 



91-13-1 

16-2-1 

20-1 

Railway Head. 

3-1 

34-1 

80-1 

75-3-1 

4.5-1 

16-4-8-2-1 

First head of drawing. 

3-1 

27-1 

4(0-1 

72-6-2-1 

Second head of drawing. 

3-1 

27-1 

4(0-1 

72-6-1 

Third head of drawing. 

3-1 

27-1 

4(0-1 

72-6-1 

Coarse Fly-Frame. 



(Continued.) 



222 



COTTON MANUFACTUKE. 



1-8 


1(0 


1-32 


9648-6-1 


1-24(0 


64-2-1 


Doubling 1-2 


Fine riy-Fraine. 


1-8 


1(0 


14-32 


56-7-1 


1-3(0 


96-24-84 


Single. 


Mule. 


1-r 


8-4-1 


1-2-30 


105-154 


1-9-36 


81-94 



40 



LOSS IN WORKING. 



Answer. 



The number sbown bj tbe draughts and doublings, and 
the number produced, are proportional to the weight of 
spread in an inverse ratio. 



Example. 

The number shown by the draughts and doublings is 
34.4, but the number actually produced is 40. Required 
the loss in working, the weight of a spread being 30 
ounces. 



LOSS EST WOEKESTG. 223 



14(0 



3(0 
34.4-8.6 



8.6 X 3 == 25.8 ounces utilized. 
30 ounces weight of a spread. 
25.8 weight utilized. 

4.2 ^=: 4 ounces and 87^ grains loss in working from 
30 ounces. 

Ans"<ver. 

The number shown by the draughts and doublings is 
34.4, but the number actually produced is 40. Required 
the percentage utilized. 

Worked out hy Cancellation. 
10(0 



1-4(0 



34.4-8.6 



8.6x10 = 86 

Answer. 



The same witJiout CancellaUon 
Dividend 100 x 34.4 



= 86 



Divisor 40 

Answer. 

The hank-roving shown by the draughts and doublings 



224 COTTON MANUFACTURE, 

is 3^, but tlie hank-roving actually produced is 4. 
Required the loss in working, the weight of a spread 
being 30 ounces. 



14 



30-7.5 
3.5 



7.6 X 3.5 26.25 ounces utilized. 

30.00 ounces weight of a spread. 
26.25 ounces utilized. 



3,T5 ounces loss in working 30 ounces. 

Answer. 

The hank-roving shown by the draughts and doublings 
is 3^, but the hank-roving actually produced is 4. Re- 
quired the percentage utilized. 

Worked out hy Cancellation. 
100-25 



1-4 



3.5 



25 X 3.5 87^ Answer. 

The same without Cancellation. 

Dividend 100 x 3.5 _ g^^ 

Divisor 4 

Answer. 



LOSS EST WORKING. 



225 



!N.B. — By the above rule the loss in working can be 
found at each and every operation, from the lapper to the 
mule. 



A railway head works successively 10 hours per day, 
and produces a No. .0455y|^ sliver. The front-roller being 
1^ inches in diameter, how many revolutions per minute 
should it make to supply a certain number of mule-spin- 
dles that produce 312 pounds of yarn per day, allowing 4: 
per cent, for loss in working ? 



189 



TO" 



100 



Diameter of front-roller, 

in inches .... 1.25 
Ratio of circumference 

to diameter • . . 3.1416 
Hours per day ... 10 
Minutes in one hour . 60 
Cent less 4 .... 96 



8.6, 'No. of sliver in 189ths. 
TOOO Grains in one pound. 
312 Pounds of yarn pro- 
duced. 
12, JL of 840. 
36 inches in one yard. 



100 Cent. 



Worked out h/ Cancellation. 



3-21-63489 



8.6 

70(00-10-l 
(Continued.) 



226 



COTTON MANUFACTURE. 



1-100 

1-1.25 
.31416-3.1416 

1(0 

1-6(0 

1-8-96 



312-39-13 

12-1 

36-6-2-1.6 



1004 



13x8.6x1.6^.31416x3 



-(go 939 1 

Answer. 



The same without Ccmcellation. 
Div. 8.6 X 7000 X 312. x 12 x 36 x 100 

Divis. 189 X 100 x 1.25 x 3.1416 x 10 x 60 x 96 



— 1«Q 93 9 1 



Answer. 



From the particulars found in the preceding example, 
find the percentage of loss in working. 

Worked out hy Ccmcellation. 
100-1 



1-3-2Y-189 



1400 

14.25 

1-.392Y-3.1416 

{Continued.) 



8.6-.86-.02 

7(000-1 

312-104-13-1 

124 

36-4-3.2-.8 



LOSS m WORKING. 



227 



140 

1-5-60 
143-559-2236(000 



11Y81-2356.2-6000 



6000 X .8 X .02 



100 



96. 
96 



4 per cent. 

Answer. 



The sa/me without Cancellation. 

Div. 100x8.6x7000x312x12x36x11781 _ gg 
Divis. 189 X 100 X 1.25 X 3.1416 X 10 x 60 x 2236000 

100 — 96 = 4 Answer. 

A drawing-frame works snccessively 10 hours per day, 
and produces a 'Eo. 182y|-^ roving. The front-roller being 
1^ inches in diameter, how many revolutions per minute 
should it make for 4 deliveries to supply a certain number 
of mule spindles that produce 312 pounds of yarn per 
day, allowing 3 per cent, for loss in working ? 



TTT 



189 



100 



Diameter of front-roll- 
er, in inches . . .1.25 



34.4, No. of sliver in 189ths. 
7000 Grains in one pound. 
312 Pounds of yarn pro- 
duced. 
12, ^ of 84-0. 
36 Inches in one yard. 



228 COTTON MANTTFACTHKE. 


Ratio of circumference 




to diameter . . 3.1416 




Hours per day ... 10 




Minutes per hour . . 60 




Number of deliveries , 4 




Cent less 3 .... 97 


100 Cent 



Worked out hy Cancellation. 



1-3-27-189 


34.4 




70(00-10-8 




312-104 


1-100 


12-2 


14.25 


36-4-1 


3.1416 




1(0 




1-6(0 




1-4 




97 


100-1 



104 X 34.4 X 8 X 2 ^ 3.1416 x 97 = 18 7||g|f^ 

Answer. 

TTie same without Cancellation. 



Dividend, 34.4 x 7000 x 31 2 x 12 x 36 x 100 . 
Divisor, 189 x 100 x 1.25 x 3.1416 x 10 

x60x4x97 



1 sYsxariT. 

-'-'-'•380 519 



Answer. 



LOSS IN WOBKING. 



229 



From the particulars found in the preceding example, 
find the percentage of loss in working. 

Worked out hy Cancellation. 
1004 



1-7-63489 


34.4 




7(0004 




312404434.3 


1400 


124 


1.25 


3644 


34416 




140 




1-5-60 




14 




8944-71552(000 


380919-76183.8 



76183.8 X 1.3 X 34.4 ^ 8944 x 1.25 x 3.1416 = 97 

100 — 97 3 per cent. 

Answer. 

The sa/me without Ca/ficellation. 
Div. 100 X 34.4 x 7000 x 312 x 12 x 36 x 380919 _ ^^ 
Divisor, 189 x 100 x 1.25 x 3.1416 x 10 x 60 x 4 
X 71552000 

100 — 97 = 3 Answer. 



A coarse fly-frame works successively 10 hours per day, 



230 



COTTON MANUFACTURE. 



and produces a ISTo. 1.092^ roving. The front-roller 
being 1^ inches in diameter, how many revolutions per 
minute should it make for 40 spindles to supply a certain 
number of mule-spindles that produce 312 pounds of yarn 
per day, allowing 2 per cent, for loss in working ? 



63 



^ of 7000 .... 100 
Diameter of the front- 
roller, in inches . .1.25 
Ratio of circumference 

to diameter . . 3.1416 
Hours per day ... 10 
Minutes in one hour . 60 
Cent less 2 .... 98 
!Number of spindles . 40 



68.8, Hank-roving in 63ds. 
YOOO Grains in one pound. 
312 Pounds of yarn pro- 
duced. 
12,JLof 840. 
36 Inches in one yard. 



100 Cent. 



Worked out hy OariGellation. 



1-9-63 


68.8 




7(0004 _ 




312 


1-100 


12-24.6 


14.25 


36-4-1 


{Cont 


inued.) 



LOSS IN WORKING 


3.1416 




1(0 




1-6(0 




98 


100-1 


14(0 





231 



312 X 68.8 X 1.6 -- 3.1416 x 98 



111 2 13294 



The sa/me without Cancellation. 

Dividend, 68.8 x YOOO x 312 x 12 x 36 x 100 _ 
Divisor, 63 x 100 x 1.25 x 3.1416 x 10 x 60 

X 98 X 40 



Answer. 



111 2132 94 



Answer. 



From the particulars found in the preceding example, 
find the number of coarse iij-frame spindles necessary to 
supply the mule-spindles. 



forked out hy Cam^cellation. 




312-104 


1-3-21-63 


68.8 




Y(000-1 


1-100 


12-2-1.6 


1-1.25 


36-12-1 


.2618-3.1416 




{Gonti 


nued.) 



232 COTTON MANUFACTmiE. 



1(0 




1-6(0 




98 


1004 


343M960(0 


30Y8Y68 



3078Y68 X 1.6 x 68.8 x 104 -^ 34344960 x 98 x .2618 iz:i= 40 

Answer. 

The same without Ca/ncellation. 
Dividend, 312 x 68.8 x 7000 x 12 x 36 x 100 x 30r8Y68 _^^ 
Divisor, 63 x 100 x 1.25 x 3.1416 x 10 x 60 x 98 x 
343449600 

Answer. 

How many pounds of cotton per day should be weighed 
on to the lapper to supply a certain number of mule-spin- 
dles that produce 312 pounds of yarn in the same time; 
allowing 14 per cent, for loss in working ? 



86 



312 
100 



312 x 100 -^ 86 = 36214 



T3 



Answer. 



How many weighings of cotton per day will it require 
to supply a certain number of mule-spindles producing 
312 pounds of yarn in the same time ; allowing 30 ounces 
to a weighing, and 14 per cent, for loss in working ? 




5 O 
_, I 
-J cr 



SPINNING. 233 



Worked out hy Ccmcellation. 




312404 


1-3(0 


16 


86 


10(0 


104:xl6xlO-r 


86 193|i 



Answer. 



The same without OanGellation 
Dividend 312x16x100 



= 193e 



Divisor 30x86 

Answer. 



SPINNING. 

The back-roller of a mule is seven-eighths of an inch in 
diameter. The change-wheel has 40, and the front-roller 
wheel 24 teeth. How many teeth should there be in the 
back-roller wheel and the top-carrier, and what should be 
the diameter of the front-roller to produce N'o. 40 from an 
8 hank-roving, run in double ; the length of the stretch 
being 60, and the rollers deliver 58 inches ? 



7, Diameter of the back- 
roller, in eighths of an 
inch. 



234 



COTTON MANUFAOTUKE. 







40 Teeth in the change- 
wheel. 






24 Teeth in the front-roller 








wheel. 


Hank-roving . . . 
Length of stretch, 


. 8 
in 


40, ITumber produced. 

2, Double-roving. 
58, Length delivered by the 


inches .... 


. 60 




rollers, in inches. 












Worhe 


d out 
7 

4(0 
24-4 
40-5 






1-8 


2 






1-6(0 


58 








58 
2 






116 
5 






580 
4 






2320 
4 


(Continued.) 




9280 
7 



SPINNING. 235 

B. . . . 10)64960 



A 8)6496 

B Y)812 

. . . 116)116 



A. 8 S', Diameter of the front-roller in eigliths of 

an inch. 

B. 10 X 7 YO Teeth in the back roller wheel. 

0. 116 =^= 166 Teeth in the top-carrier. 

Answer. 

From the particulars found in the preceding example, 
find the number produced. 

Worked out hy Ocmcellation. 



1-2 
l-Y 

14(0 
1-3-24 

1-29-58 



8-24 

84 

7(04 

116-58-2 

60-20 



20 X 2 40 Answer. 

The sa/me without Cancellation. 
Dividend, .... 8x8x70x116 x60 _ ^^ 

Divisor 2x7x40x24x58 

Answer. 



236 



COTTON MANUFACTUBE. 



From tlie particulars found in tlie preceding example, 
find the hank-roving. 



Worked out hy Cancellation. 




4(0-1 


1-2-8 


7-1 


1-Y(0 


4(0-1 


1-29416 


24-4 


1-6(0 


58-2 




2-1 


4x2 — — 8 hank-roving. 



Answer. 



The same witJiout Cancellation. 

Dividend . . . 40x7x40x24x58x2 . 
Divisor .... 



8 X 70 X 116 X 60 



Answer. 



From the particulars found in the preceding example, 
find the diameter of the back-roller. 



Worked out hy CoMcdlation. 

1-2 8-2-1 
1-4(0 

8-2-1 
{Continued.) 



SPINNING. 



237 



14(0 
1-24-24 

1-58 



7(0 

116-584 

6(04 



4- of an incli. 



Answer. 



Dividend 
Divisor . 



The same without Cancellation. 
. 8 X 8 X 70 X 116 X 60 



2 X 40 X 40 X 24 X 58 



7 = 1 of an inch. 



Answer. 



Erom the particulars found in the preceding example, 
find the diameter of the front-roller. 



Worked out hy Cancellation 



1-2-8 



1-7(0 

1-58-116 

1-3-6(0 



2-1 

4(0-1 

7-1 

4(0-2-1 

24-8 
58-1 



-I of an inch. 



Answer. 



The sa/me without Cancellation. 
Dividend . 2x40x7x40x24x58 
Divisor . . 8 x 70 x 116 x 60 



= 8 = f of an inch. 



Answer. 



238 



COTTON MANUFACTUEE. 



Froin tlie particulars found in the preceding example, 
find the number of teeth in the back-roller wheel. 

Worked out hy Cancellation. 

4(0-2 
2-1 
40-5 
1-8 7 
1-58416 24-34 
l-2-6(0 584 



Yx5x2 



TO 



Answer. 



The same without Cancellation. 

Dividend . . . 40 x 2 x 40 x T x 24 x 58 
Divisor .... 



= 70 



8x8x116x60 



Answer. 



From the particulars found in the preceding example, 
find the number of teeth in the change-wheel. 



Worked out hy Cancellation, 

7040 
1'2 8-2 
14(0 
{Continued.) 



sphstning. 



239 



1-7 
1-3-24 

1-58 



116-58-1 
6(0-2 



10x2x2 



40 



Answer. 



The same without Ccmcellation. 
Dividend . . . . 70x8x8x116x60 



= 40 



Divisor 2x40x7x24x58 

Answer. 

From the particulars found in the preceding example, 
find the number of teeth in the top-carrier. 

Worked out hy Ccmcellation. 

24-34 
2-1 

4(04 

1-2-8 74 
1-7(0 4(0-2 
1-3-6(0 58 



58x2: 



116 



Answer. 



The so/me without Cam.cellat/ion. 
Dividend . . 24x2x40x7x40x58 
Divisor . . . 8x8x70x60 



= 116 



Answer. 



240 



COITON MANUFACTUKE. 



From the particulars found in the preceding example, 
find the number of teeth in the front-roller wheel. 

Worked out hy Ccmcellation. 
116-2 



1-2 

14(0 
1-7 

14(0 
1-58 



8-2 

8-24 
7(04 
6(0 



6x2x2: 



24 



Answer. 



The same witJiout Cancellation. 
Dividend . . . . 116x8x8x70x60 



= 24 



Divisor 2x40x7x40x58 

Answer. 



From the particulars fomid in the preceding example, 
find how many inches the rollers deliver per stretch. 



Worked out hy Cancellation. 
6(04 
1-2 8-24 
14(0 
{ContMiued.) 



SPINNDSTG. 



24:1 



1-7 

14(0 

14-24: 



8-2 

7(04 

116-29 



29 X. 2 



58 inclies. 



Answer. 



The same witliout Ca/ncellation 

Dividend . . 60 x 8 x 8 x YO x 116 
Divisor . . 2x40x7x40x24 



= 58 inclies. 



Answer. 



From the particulars found in the preceding example, 
find the length of the stretch. 

Worked out hy CanGellaUon. 
58-1 
2-1 
40-5 
1-8 7-1 
1-7(0 4(0 
1-2-116 24-3 



5x4x3 



60 inches. 



Answer. 



The same without Cancellation. 
Dividend . 58x2x40x7x40x24 
Divisor . . 8 x 8 x 70 x 116 



= 60 inches. 



Answer. 



242 COTTON MANUFACTURE, 



The back-roller is seven-eighths, and the front-roller 
eight-eighths of an inch in diameter. The front-roller 
wheel has 24, the top-carrier 116, the change-wheel 40, 
and the back-roller wheel TO teeth. The rollers dehver 
58, and the length of the stretch is 60 inches. Required 
the total draught at the mnle. 



Worked out hy Cancellation. 



1-r 


844 


1-4(0 


7(04 


1-642-24 


116-24 


1-58 


6040 



10 Answer. 



The sa/ine without CoMceUation. 
Dividend 8x70x116x60 



= 10 



Divisor . . . . . . 7x40x24x58 

Answer. 

The number spun is 40 from an 8 hank-roving, run in 
double. Required the draught. 

Worked out hy Cam,ceTlation. 
40-5 



5x2 ■■ 10 Answer. 



SPDfNING. 243 

The same without Ca/ncellation. 

Dividend 40 x 2_ -.^ 

Divisor 8 

Answer. 

The back-roller is seven-eightlis, and the front-roller 
eight-eiglitlis of an inch, in diameter. The front-roller 
wheel has 24, the top-carrier 116, the change-wheel 40, 
and the back-roller wheel 70 teeth. Required the draught 
at the rollers. 

Worked out hy Cancellation. 



1-7 

14(0 
1-3-24 


84 

7(04 

116-29-9I 


9 


f 



Answer. 



The same without Cancellation. 
Dividend 8x70x116 



= n 



Divisor 7x40x24 

Answer. 

The length of the stretch is 60 and the rollers deliver 
58 inches. Required the di'aught at the carriage. 



244: COTl'ON AIANUFACTUKE. 



Worked out hy Cancellation. 
1-58 I 60-1^ 



1^ Answer. 



The dranglit at the rollers is 9f , and the draught at the 
carriage is 1^. Required the total draught at the mule. 

Worhed out hy CanGellat/ion. 



1-3 

1-29 



294 
30-10 



10 Answer. 



The same without Ga/nGeUation. 
Dividend 29 x 30 



10 



Divisor ......... 3 x 29 

Answer. 

The length of the stretch is 60, and the rollers deliver 
58 inches. Required the gain of the carriage per stretch. 



60 
58 



2 inches. 

Answer. 



SPINNING. 215 

The draught at the rollers is 9f . The length of the 
stretch is 60, and' the rollers deliver 58 inches. Eequired 
the number spun from an 8 hank-roving, run in double. 

Worked out 'by Ccmcellation. 



1-2 

1-3 

1-2-58 



84-2 

294 

60-20 



20 X 2 = 40 

Answer. 



The same without Ccmcellation. 
Dividend . . 8x29x60 



= 40 



Divisor 2 x 3 x 58 

Answer. 

If IN^o. 40 is spun from a 4 hank-roving, with a change- 
wheel containing 40 teeth, how many teeth should there 
be in the change-wheel to spin No. 60 from a 7-|- hank- 
roving ? 

Worked out l>y Cancellation. 

40 
14 Y.54.25 
1-6(0 4(0-1 

40 x 1.25 50 Answer. 



246 



COTTON MANUFACTURE. 



The same without Ca/iicellation. 

Dividend 40xY.5x40 , 

Divisor 



50 



4x60 



Answer. 



A set of cops weighs 11 lbs., and has on 630 stretches. 
Length of stretch, 60 inches ; number of cops in the set, 
352. Keqtdred the average number. 



Worked out ly Cancellation. 




'352-32-8 


1-3-36 


60-5 


l-21-84(0 




141 






63(0-21-1 



8x5 = 



40 



Answer. 



The same without Ca/ncellation. 
Dividend 352x60x630 



40 



Divisor 36x840x11 

Answer. 

From the particulars found in the preceding example, 
find the number of stretches in the set. 

WorTced out hy Cancellation. 
11-1 
40-5 
(^Continued.) 



sPEsnsriNG. 



247 



14-32-352 

1-6(0 



84(0-21 
36-6 



21 X 6 X 5 



630 



The same without Cancellation. 
Dividend .... 11 x 40 x 840 x 36 
Divisor 



Answer. 



= 630 



352 X 60 



Answer. 



From the particulars found in the preceding example, 
find the length of the stretch. 

Worked out hy Cancellation. 
11-1 



1-4-32-352 



1-21-63(0 



40-5 

84(0-21-1 
36-12 



12 X 5 60 inches. 

The sa^ne without CamjCellation. 
Dividend . . . 11 x 40 x 840 x 36 
Divisor . . . 352x630 



Answer. 



60 inches. 



Answer. 



From the particulars found in the preceding example, 
find the number of cops in the set. 



248 



COIiTON MAITUFACTTIKE. 



Woi'lced out hy GancellaUon. 




11 




4(0 


l-r-21-63(0 






84(0-284 


1-6(0 


36-6-2 



11x4x4x2^=352 



Answer. 



TJie same without Cancellation. 
Dividend .... 11x40x840x36 . 
Divisor 



352 



630 X 60 



Answer. 



From tlie particulars found in tlie preceding example, 
find the weight of the set. 



Worlced out hy Cancellation. 




352-88-22-11 


1-21-84(0 






63(0-21-1 


1-4(0 




1-2-6-36 


6(0-1 



11 lbs. 



Answer. 



SPINNING. 



24:9 



The sa/me without Cancellation. 
Dividend 352x630x60 



= 11 



Divisor 840x40x36 

Answer. 



The power furnislied for driving mules is sufficient to 
drive tliem 3 stretches per minute, and they utilize -^ of 
the same. Required the product per spindle per day of 
12 hours, the length of the stretch being 60 inches. 



Inches in one yard 



Power furnished . 
Yards in one hank 



36 



15 

840 



60, Length of stretch, in 
inches. 
3 Stretches per minute. 
60 Minutes in one hour. 
12 Hours per day. 
14, Power utilized. 



Worked out hy Oam^Gellation. 



1-3-36 


60-5-] 




34 




6(0-2 




124 


1-345 


14-2 


l-Y-84(0 





2x2 



4 hanks. 



Answer. 



250 COTTON MANUFACTURE. 

Tlie same without Cancellation. 
Dividend . . 60 x 3 x CO x 12 x 14 _ ^ ^^^^^^^ 
Divisor ... 36x15x840 

Answer, 

A pair of mnles, each containing 352 spindles, produce 
4 hanks per spindle per day. How^ many hanks will that 
be per week, and what will the spinners' wages amount to, 
at 4|- cents per 100 hanks ? 

352 Spindles in each mule. 

2, ISumber of mules. 

4, Product per spindle per 
day, in hanks. 

6 Days per week. 
4.5 Cents per 100 hanks. 

352 X 2 X 4 X 6 ■ 16896 hanks per week. 

16896x4.5 -r- 100 = $7.60^ 

Answet*. 

To find the requisite number of turns of twist per inch 
for warp and filling. 

Rule. 
For warp, multiply the square root of the number by 
8f , and for filling, by 3|-, and the product will be the 
number of tm-ns of twist per inch required. 



SPINNING. 251 

Examjples. 
How many turns of twist per incli will be required for 
]Sro. 40 warp ? 

6)40(6.324-1- 
36 



123)400 
369 



1262)3100 
2524 



12644)57600 

50576 



7024 



6.324 
3.75 

31620 

44268 
18972 

23.71500 



Answer. 



252 COTTON MAJSrUFAOTUEE. 

How many turns of twist per inch will be required for 
No. 40 filling ? 

6)40(6.324+ 
36 



123)400 
369 



1262)3100 

2524 



12644)57600 

505Y6 



Y024 



6.324 X 3.25 = 20.553 Answer. 

Another way to find the requisite turns of twist per 
inch of yarn : — Admitting that 25 turns of twist per inch 
of yarn is sufficient for JSTo. 50 warp, and the same for 
No. 60 filling, and that the twist in different numbers of 
yarn is as the square of the twist to the number of the 
yarn, we get the following 

Rule. 
As No. 50 is to the square of 25, so is the giv^en No. to 
the square of the twist per inch required. 



SPINNING. 253 



JExample. 



How many turns of twist per incli is required for ISTo. 
40 warp ? 



1-5(0 



25 X 25 r= 625425 
4(0 



125 
4 

2)5^00(22.36+ Answer. 

4 

42)100 
84 



443)1600 
1329 



4466)27100 
26796 



304 



How many turns of twist per incli is required for Ko. 
40 filling? 



254 COTTOX MANUFACTUKE. 



1-6(0 



25 X 25 = 625 
4(0-.6666 + 



625 



33330 
13332 
39996 

2)4^16;62^50(20.41+ Answer. 
4 



404)1662 
1616 

4081)4650 
4081 



569 



N.B. — There are many other rules in use for finding the 
requisite twist per inch of yarn, each of which has its 
advantages, but the above are generally considered the 
simplest and best. 

The pracHcal rule is, to try the yam by breaking it. 
If the fibres draw out of warp instead of breaking off 
short, it has not twist enough ; for filling, that need not 
be minded, if it works well in the mule and the loom. 




f^. 



m 



'^' ^ 



^1 



M A NTJFACTUBING. 



255 



MAKTJFACTUEIIsrG. 



How many hanks of yarn will be required to make a 
warp of 14 cuts, each 42 yards long, 30 inches wide at the 
reed, and 64 threads to the inch, allowing Jg- for shrinkage 
in weaving ? 

Worked out hy Cancellation. 



l-2'84(0 



42-1 
3(0 
64 
14-Y 



64xYx3+iig 



1418.66+ Answer. 



Dividend 
Divisor . 



The same without Cancellation 
. 42 X 30 X 64 X 14 



840 



+ iV = 1418.66 + 
Answer. 



■ How many hanks of filling will be required to fill a 
warp of 14 cuts, each 42 yards long, 30 inches wide at the 
reed, and 64 picks to the inch, allowing -^ for waste? 

Worked out hy Cancellation. 



l-2-84(0 



424 

3(0 

64 

14-7 



64x'7x3+JL 



"BIT 



1366.4 



Answer. 



256 COTTON MANUFACTUEE. 

The same without Ccmcellation. 

Dividend . . . . 42 x 30 x 64 x 14 , . ., o^/; a 

+ eV = 1366.4 

Divisor .... 840 

Answer. 

In 1418.666 hanks of l!^o. 36, hovr many pounds ? 

Wo7'ked out hy Cancellation. 

1-4-32 I 1418.6664YT.333-44.333 

44.333 

Answer. 

In 1366.4 hanks of I^o. 30, how many pounds ? 

Worked out hy Cancellation. 

1-3-36 I 1366.4413.866-3Y.955 

37.955 

Answer. 

If 44.33 + pounds of yarn be sufficient for a warp of 14 
cuts, each 42 yards long, including shrinkage in weaving, 
and 37.955 pounds of filling be sufficient to fill the same 
including waste, what will be the total weight of warp and 
filling necessary to make the 14 cuts ? 



MANUFACTUSmG. 25Y 

M.333 

3Y.955 



82.288 pounds. 

Answer. 

If 82.288 pounds of warp and filling liave been used 
in making 14 cuts of cloth, each 42 yards long, how many 
yards per pound is utilized ? 

Worked out hy GoMceUaUon. 

42-.5104 
14 

1-82.288 



14 X .5104 = 7.1456 

The sa/me without (Ja/nceUaUon. 
Dividend 42x14 



Answer. 



= 7.1466 



Divisor 82.288 

Answer. 

Another way to find the number of yards per pound 
utilized from the same particulars : — 



258 



COTTON MANUFACTU-RE. 



64+,5V Picks =: 65.666 
G4 + _i^ Reed = 67.555 



133.221 



Width of the reed, in 
inches .... 30 

Warp and filling in- 
cluded 2 



36 No. of filling. 
32 No. of warp. 

68 



840 Yards in one hank. 



Worked out by CcmGellation. 






67.555 



1433.221 

1-3(0 

1-2 



36 
32 

68-.51 + 

84(0-28-14: 



14 X. 51 + = 7.14+ 



Answer. 



Find the number of yards of cloth per pound from the 
following particulars : — 

Count of reed 72 

Width of reed 42 inches. 



MANUFACTURING. 



259 



Picks per inch 100 

Counts of filling 40 

Counts of warp 32 

Shrinkage of warp in weaving -j^^- 

Worhed out hy Cancellation. 



Ko. of filling . . 



14(0 
142 



42-3.5, Width of reed. 
100*25 Picks per inch. 

10(0 



25 X 10 X 3.5 = 875 grains weight of filling in one yard 
of cloth. 



Ko. of warp 



14-32 
1-12 



42-5.25, Width of reed. 
72-6, Count of reed. 



100-25 



25 x6x5. 25 +-ji(j- = 866.25 grains weight of warp in 
one yard of cloth. 



866.25 
875.00 



174.25)7000.00(4+ yards. 
6965.00 



35.00 



Answer. 



260 



COTTON MANUFACTUEE. 



Another way to find the number of yards of cloth per 
pound from the same particulars : 

Worked out hy Cancellation. 



'^2+1^ 



100 - 
z79.2 



1-179.2 
142 

1-2 



40 
32 

72-.4+ 
840-2040 



10 X. 4+ 



4+ 



Answer. 



If it requires 866.25 grains of warp to make one yard 
of cloth, as seen in a preceding example, how many 
pounds will be required to make a warp of 10 cuts, each 
40 yards long ? 

Worhed out hy Ca/ncellation. 
1(0 



i-T-ro(oo 



4(0-.4 
866.25-123.75 



123.75 X .4 



49.5 



Answer. 



The same without Cancellation. 
Dividend .... 10 x 40 x 866.25 , 
Divisor 7000 



49.5 



Answer. 



MANUFACTUKtNG. 261 

If it requires 8Y5 grains of filling to make one yard of 
cloth, how many pounds will it require to make 10 cuts, 
each 40 yards long ? 

Worked out hy CancellaUon. 
1(0 



i-r-7o(oo 



4(0-.4 

8Y5425 



125 X .4 == 50 Answer. 



The same without Cancellation. 
Dividend 10x40x875 



= 50 



Divisor 7000 

Answer. 

If it requires 49|- pounds of warp, and 50 pounds of 
filling, to make 10 cuts of cloth, each 40 yards long, what 
is the total weight of warp and filling required ? 



49.5 
50.0 



99.5 pounds. 



Answer. 



How many hanks of yarn will be required to make a 
warp of 10 cuts, each 40 yards long, to be woven in a 72 



262 



COTTON MA.NUFACTUEE. 



reed, 42 inches wide, making an allowance of -^ for 



shrinkage in weaving. 




Worked out hy Cancellation. 




1(0 




40 




42-6 




Y2-6 


l-Y-84(0 





40 X 6 X 6 + Jj- = 1584 Answer. 



The same without Cancellation. 
Dividend . . . 10 x 40 x 42 x 72 j_ ^ ^^g^ 



Divisor 



840 



Answer. 



If 1584 hanks of yarn weigh 49|- pounds, what is the 
number ? 



Worked out hy Cancellation. 
1584-32 



1-49.5 

1-7(000 

1-12 



84(0-12-1 



1(00 



32 



Answer. 



MANUFACTURING. 263 



The sarnie without Ccmcellation. 
Dividend 1584x840x100 



32 



Divisor 49.5x7000x12 

Answer. 

In 10 cuts of clotli, each 40 yards long, woven in a reed 
42 inches wide, 100 picks to the inch, how many hanks 
of filling? 

Worked out hy CanceUat/lon. 

1(0 
4040 

42-2 



l-21-84(0 



100 



100 x 10 x 2 = 2000 

Answer. 

The sa/me without Ccmcellation. 

Dividend .... 10x40x42xl00 _ ^^^^ 

Divisor 840 

Answer. 

If 2000 hanks of filling weigh 50 pounds, what is the 
number ? 



264: COTTON MANUFACTURE. 



Worked out hy Cancellation. 



1-50 

1-7(000 

142 



2(000 
84042040 



100-2 



10x2x2=40 



Answer. 



The same witJiout Ca/ncellation. 
Dividend 2000x840x100 



40 



Divisor 50x7000x12 

Answer. 

Find tlie number of yards per pound of clotli from the 
following particulars : 

Counts under tlie glass, QQ threads of warp and 80 of 
filling per inch. 

"Width of reed .... 33 inches. 

Counts of warp .... 33 

Counts of filling .... 40 
Shrinkage in weaving of warp and filling, ■^. 



MANUFACTURING. 



265 



Worked out hy Cancellation. 

324, Width of reed. 
66-5.5 Threads of warp per 
inch. 



Counts of warp 



1-33 
1-12 



100 



100 X 5.5 +^ 584.3Y5 grains weight of warp in one 

yard of cloth. 



Counts of filling 



140 
1442 



3341, Width of reed. 
80-2 Picks per inch. 



100-25 



25 X 11 x2+-jig- = 584.375 grains weight of filling in 
one yard of cloth. 



584.3Y5 

584.3Y5 



1168.75(0)7000.00(0(5.9 + 
5843.75 



Answer. 



1156.250 
1051.875 



104.375 



266 



COTTON MANUFACTURE. 



Another way to find the number of yards of cloth per 
pound from the same particulars : 



Reed 
Picks 



Worked out hy CcmGellation. 



80 



1-2-146 

1-33 

1-2 



33 Warp. 
40 Filling. 

73-1 



840420-210-6.36 



6.36 less iV 



6.9 + 



AnSwer. 



How many pounds of I^o. 50 yarn will it take to make 
a beam of 10 cuts, according to the following particulars : 



Length of cuts . 


. . . 60 yards. 


Count of reed .... 92 


Width of reed .... 42 inches 


Shrinkage in weaving . . -^ 


Worked out hy Ccmcellation. 




1(0 




6(04.2 




42-3.5-.5 


{Conti 


nued.) 



TVrANUFACTUBING. 



267 



1-5(0 

l-Y-84(0 



92 



92xl.2x.5+JL 



60.T2 



Answer. 



The same without Cancellation. 

Dividend . . . 10x60x42x92 
Divisor .... 50x840 



+J^=60.72 



Answer. 



How many pounds of 1S.Q. 60 filling will it take to fill 
10 cuts, according to the following particulars ? 



Length of cuts . 
Width of reed . 
Picks per inch . 



60 yards. 
42 inches. 
108 



Worked out hy Gam^cellat/ion. 

1(0 

604 

42-6 



l-12-84(0 
1-60 



108-9 



9x6 



54 



Answer. 



26S 



COTTON MANUFACTTJKE. 



The same without Cwncellation. 

Dividend 10x60x42x108 

Divisor 



= 54 



840 X 60 



Answer. 



If there are 60. Y2 pounds of warp and 54 pounds of 
filling in 10 cuts of cloth, each 60 yards long, how many 
yards of cloth are there to the pound ? 

Worked out hy Cancellation. 
60.72 
54 



141.472-114.Y2 



104 

60-5.2 + 



5.2 + 



Answer. 



rind the number of yards per pound of cloth from the 
following particulars : 



Count of reed . . 


. 92 


"Width of reed . . 


42 inches. 


Picks per inch . . 


. 108 


Counts of warp . . 


. . 50 


Counts of filling 


. . 60 



Shrinkage of warp in weaving, ^. 



MASrUFACTUKING. 



269 



Worked out hy OmiGellation. 
42-3.5 



1-50 
142 



92 
100-2 



92 X 3.5 X 2+ J^ = 708.4 grains weight of warp in one 



yard of cloth. 



1-6(0 
1-12 



42-Y 
108-9 

10(0 



10 X 9 X Y 630 grains weight of filling in one yard of 

cloth. 

708.4 
630.0 



1338.4)7000.0(5.2+ 
6692.0 



Answer. 



308.00 
267.68 

40.32 



Another way to find the number of yards of cloth per 
pound from the same particulars : 



270 



COTTON MAJSrUEACTURE. 



Wo7'Tced out l)y Cancellation. 



Eeed92+-jV 


101.2 


50 Warp. 




Picks . . . 


108 


60 Filling. 






1-209.2 


110-.52 + 




"Width of reed , 


. . 142 






Warp and filling 


. . 1-2 


840-2040 






10X.52+ 


5.2 + 


Answer. 



Another way to find the number of yards of cloth per 
pound : 

Rule. 
Cut from the cloth a piece two inches square. The 
weight of this multiplied by half the width of the cloth, 
gives a product which, divided into 389, equals the num- 
ber of yards per pound. 



Example. . 

In the above example the cloth is 42 inches wide, con- 
sequently, one yard contains 42 x 36. =1512 square inches, 
and weighs Y08.4 + 630. =1338.4 grains. A piece of cloth 
2 inches square contains 2 x 2=4 square inches. Hence, 
1338.4x4^1512=3^3^ grains weight of the 4 square 
inches. 



manhfactueing. 



271 



If 4 square inches of cloth weigh S^^ grains, how 
many yards are there to the pound ? 

TSJ" "R Q 1 2- 2 — 669:2 

Worked out hy Cancellation. 



669.2 
1-7-21 



189-63-9 

389 



389x9-^669.2 



The sarnie without Cancellation 
Dividend 189 x 389 



Divisor 669.2x21 



5.2 yards. Answer. 

ation. 

= 5.2 yards. 



Answer. 



A piece of lawn is 36 inches wide, and counts, under the 
glass, 80 X 80. The filling is ISTo. 80, and the warp ISTo. 
75 ; how many yards are there to the pound, admitting 
the warp and filling to shrink -^ in weaving ? 

Worked o%tt hy Cancellation. 
36-34 



1-3-75 
142 



80 
1004 



80 X 4+^ 336 grains weight of warp in one yard of 

cloth. 



272 



COTTON MANUFACTURE. 



1-80 
142 



36-3 
80-1 

100 



100 X 3+^ 315 grains weight of fiUing in one yard 



of cloth. 



336 
315 

651)7000(10.7+ 
651 



Answer. 



4900 
4557 

343 

Another way to find the number of yards of cloth per 
pound from the same particulars : 

Worked out hy Cancellation. 



Eeed 
Picks 



80+^: 

80 + 



?T 



84 
84 



1-2.4468 
Width of cloth . . 1-3-36 
Warp and filling . . 1-2 



80 Warp. 
75 Filling. 

155-77.5-32.240.7+ 



840-70-1 



10.7 



Answer. 



MA^SrUFACTIIRING. 



273 



Suppose a loom to work successively at the rate of 140 
picks per minute, how long would it be weaving a cut of 
42 yards with 100 picks per inch ? 



Worked out hy Cancellation. 




42-3-1 




36-18 


144(0 


1(00 


l-2-6(0 




18 h( 


Durs. 



The same without Ca/rhcellation. 
Dividend .... 42 x 36 x 100 
Divisor 140x60 



Answer. 



= 18 hom's. 



Answer. 



If the power furnished for driving a loom be sufficient 
to drive it 140 picks per minute, and the actual product 
is 34,125 yards, containing 100 picks per inch, in 18 hours, 
how much per cent, of the power does it utilize ? 

Worked out hy Cancellation. 





100-50 




34.125-4.875-1.625 




36-2-1 


1-M4(0 


1(00 


1-18 




l-3-6(0 




50x1,6^5 


81.25 per cent. Answer. 



274 COTTON MANUFACTURE. 



The same without Camcellation. 

Dividend . . . 100x34.125 x 36 xlOO _ g^ 25 
Divisor ... 140x18x60 

Answer. 



Suppose a loom to work successively at the rate of 128 
picks per minute, how long will it be weaving a cut 46 
yards long, containing 80 picks per inch ? 

Worked out iy Ca/ncellation. 
46-5.Y5 



1-846-128 
1-5-60 



36-3 
80-10-2-1 



5.T5 X 3 17.25 17 hours 15 minutes. 

Answer. 



The same without Ganficellation 
Dividend 46 x 36 x 80 



= 17.25 



Divisor 128x60 

Answer. 

If the power furnished for driving a loom is sufficient 
to drive it 128 picks per minute, and the actual product is 
28f yards, containing 80 picks per inch, in 12 hours, how 
much per cent, of said power does it utilize ? 



WAMUJ^'ACTURING. 27 


Worked out hy Cancellation. 




100-25-6.25-3425 




28.75 




36-34 


1446428 


8(04 


142 




l-2-6(0 




28.75 X 3425 


89.84375 per cent. 



The same without Cancellation 
Dividend . . 100 x 28.75 x 36 x 80 
Divisor. . . 128x12x60 



Answer. 



= 89.84375 



Answer. 

Admitting the power furnished for driving looms to be 
sufficient to drive them 120 picks per minute, and that 
they utilize 90 per cent, of the same, the cloth to be made 
into cuts each 45 yards long, containing 80 picks per inch, 
what will be the monthly wages of a five loom weaver at 
36 cents per cut, allowing 12 hours to the day, and 24 
working days to the month ? 

Worked out hy Cancellation. 
364 



1-8(0 



12(0 



{Continued^ 



276 



COTTON MANXJFACTUKE. 



1(00 

1-545 
1-36 



6(0 
12 
24-3 
5-1 

9(0-1 



12x12x6x3 



$25.92 



Answer. 



Dividend 
Divisor . 



The sa/me without Cancellation. 
. . 36 X 120 X 60 X 12 X 24 X 5 X 90 



80x100x45x36 



X $25.92 



Answer. 



Admitting the power furnished for driving looms to be 
sufficient to drive them 118 picks per minute, and that 
they utilize 75 per cent, of the same, the cloth to be made 
into cuts, each 60 yards long, containing 108 picks per 
inch, how much per cut should be paid to a three-loom 
weaver to make $36 per month, allowing 12 hours to the 
day, and 24 working days to the month ? 

Worked out hy Cam,Gellation. 
36-3-1 
1-59418 108-9-3 
1-60 
{Contimied.) 



MANUFACTUBING. 



277 



142 

1-2-24 

1-3 

1-3-75 



1004-2 
604 

3648-^ 



3x2x-^. 



'TW 



The scmie without Cancellation. 

Dividend . . . 36x108x100x60x36 
Divisor. . . . 118x60x12x24x3x75 



Answer. 



= $1.83^ 



T? 



Answer. 

From the particulars found in the preceding example, 
find the weaver's monthly wages. 



Worked out Iry Cancellation. 




1-59 


1084 . . . 


(V^of$l.) 


1408 


118-2 

604 

12-1 

24-6 

34 




14400 


75-3 




1-60 






1-3-36 







6x2x3 



$36. 



Answer, 



278 COTTON MANUFACTURE. 

Tlie same without Ca/acellat/lon. 
Dividend . . . 108x118x60x12x24x3x75 



= $36. 



Divisor . . . 59x108x100x60x36 

Answer. 

Admitting the labor and skill required to weave 14 twill 
cuts per loom, on five looms per month, to be equal to 
that required to weave 16 cambric cuts per loom on 4 
looms in the same time, and the price paid for the cam- 
bric 39 cents, and the twill 28 cents per cut, how much 
per cut should be advanced on the twills to make the 
monthly wages of the weavers equal, if the cambric is 
advanced to 42 cents per cut % 

Worked out hy Cancellation. 
42-6 



1-5 
1-744 



4-.8 
16-8 



8 X 6 X .8 — 28 10.4 cents. 

Answer. 

The same without Cancellation. 

Dividend. . . i2x4><16_ 28 ^10.4 cents. 
Divisor. ... 5x14 

Answer. 



MAJSrUFACTUKING. 279 

From the particulars found in the preceding example, 
find the monthly wages of the twill and cambric weavers 
at the advanced price. 

Twill 38.4 X 14 X 5 :=: $26.88 

Cambric 42x16x4 =$26.88 

Answer. 

Admitting the labor and skill required to weave 16 
cambric cuts per loom on 4 looms per month, to be 
equal to that required to weave 14 twill cuts per loom on 
5 looms in the same time, and the price paid for the twill 
is 38.4 cents per cut, how much per cut should be paid for 
the cambric to make the monthly wages of the weavers 
equal ? 



Worked out hy Oancellat/ion. 






38.4-4.8-1.2 




1-4 


5 




1-8-16 


14-7 




Tx5xl.2 = 


— 42 cents. 





Answer. 

The sa/me without Cancellation. 

Dividend 38.4x5x14 .^ 

= 42 cents. 

Divisor 4x16 

Answer. 



280 corroN manufacture. 

If one weaver weaves 16 cambric cuts per loom per 
month on 4 looms, and another weaves 14 twill cuts per 
loom on 5 looms in the same time, and an advance of 6 
cents per cut is made on the twill, how many cents per 
cut should the cambric be advanced to make the monthly 
advance of the weavers' wages equal? 



Worked out h[ 

146 
1-2-4 


1/ Cmicellation. 
6-3 

14-T-.43Y5 
5 


5 X 3 X .43Y5 z= 


— 6-^ cents. 



Answer. 

The sa/me without Cancellation. 
Dividend ...... 6x14x5 ^ g_,^ ^^^^^^ 

Divisor 16x4 

Answer. 

From the particulars found in the preceding example, 
find the monthly advance in the weavers' wages. 

Cambric 6^^x16x4 $4.20 

TwiU 6x14x6 =$4.20 

Answer. 



CAEDESTG. 



281 



SLIYEK TABLE, 

Showing the size of sliver from "No. .01 to .09, by the 
weight of 6 yards, in grains. 



Number. 


Grains. 


Number. 


Grains. 


Number. 


Grains. 


.01 


5000 


.037 


1351 


.064 


781 


.011 


4545 


.038 


1316 


.065 


769 


.012 


4167 


.039 


1282 


.066 


758 


.013 


3846 


.04 


1250 


.067 


746 


.014 


3571 


.041 


1220 


.068 


735 


.015 


3333 


.042 


1191 


.069 


725 


.016 


3125 


.043 


1163 


.07 


714 


.017 


2941 


.044 


1136 


.071 


704 


.018 


2778 


.045 


1111 


.072 


694 


.019 


2632 


.046 


1087 


.073 


685 


.02 


2500 


.047 


1064 


.074 


676 


.021 


2381 


.048 


1042 


.075 


667 


.022 


2273 


.049 


1020 


.076 


658 


.023 


2174 


.05 


1000 


.077 


649 


.024 


2083 


.051 


980 


.078 


641 


.025 


2000 


.052 


962 


.079 


633 


.026 


1923 


.053 


943 


.08 


625 


.027 


1852 


.054 


926 


.081 


617 


.028 


1786 


.055 


909 


.082 


610 


.029 


1724 


.056 


893 


.083 


602 


.03 


1667 


.057 


877 


.084 


595 


.031 


1613 


.058 


862 


.085 


588 


.032 


1563 


.059 


847 


.086 


581 


.033 


1515 


.06 


833 


.087 


575 


.034 


1471 


.061 


820 


.088 


568 


.035 


1429 


.0^2 


806 


.089 


562 


.036 


1389 


.063 


794 


.09 


556 



282 



COTTON MANUFACTUKE. 



SLIVER TABLE, 



Showing the size of sliver from 'No. .091 to No. .236, by 





the weight of 6 yards, in 


grains. 




Number. 


Grains. 


Number. 


Grains. 


Number. 


Grains. 


.091 


549 


.134 


373 


.186 


269 


.092 


543 


.136 


368 


.188 


266 


.093 


538 


.138 


362 


.19 


263 


.094 


532 


.14 


357 


.192 


260 


.095 


526 


.142 


352 


.194 


258 


.096 


521 


.144 


347 


.196 


255 


.097 


515 


.146 


342 


.198 


253 


.098 


510 


.148 


338 


.2 


250 


.099 


505 


.15 


333 


.202 


248 


.1 


500 


.152 


329 


.204 


245 


.102 


490 


.154 


325 


.206 


243 


.104 


481 


.156 


321 


.208 


240 


.106 


472 


.158 


316 


.21 


238 


.108 


463 


.16 


313 


.212 


236 


.11 


455 


.162 


309 


.214 


234 


.112 


446 


.164 


305 


.216 


231 


.114 


439 


.166 


301 


.218 


229 


.116 


431 


.168 


298 


.22 


227 


.118 


424 


.17 


294 


.222 


225 


.12 


417 


.172 


291 


.224 


223 


.122 


410 


.174 


287 


.226 


221 


.124 


403 


.176 


284 


.228 


219 


.126 


397 


.178 


281 


.23 


217 


.128 


391 


.18 


278 


.232 


216 


.13 


385 


.182 


275 


.234 


214 


.132 


379 


.184 


272 


.236 


212 



CARDING. 



283 



SLIVEK TABLE, 

Showing the size of sliver from 'No. .238 to No. 1, by the 
weight of 6 yards, in grains. 



Number. 


Qratns. 


Number. 


Grains. 


Number. 


Grains. 


.238 


210 


.292 


171 


.53 


94 


.24 


208 


.294 


170 


.54 


93 


.242 


207 


.296 


169 


.55 


91 


.244 


205 


.298 


168 


.56 


89 


.246 


203 


.3 


167 


.57 


88 


.248 


202 


.31 


161 


.58 


86 


.25 


200 


.32 


156 


.59 


85 


.252 


198 


.33 


152 


.6 


83 


.254 


197 


.34 


147 


.62 


81 


.256 


195 


.35 


143 


.64 


78 


.258 


194 


.36 


139 


.66 


76 


.26 


192 


.37 


135 


.68 


74 


.262 


191 


.38 


132 


.7 


71 


.264 


189 


.89 


128 


.72 


69 


.266 


188 


.4 


125 


.74 


68 


.268 


187 


.41 


122 


.76 


66 


.27 


185 


.42 


119 


.78 


64 


.272 


184 


.43 


116 


.8 


63 


.274 


182 


.44 


114 


.82 


61 


.276 


181 


.45 


111 


.84 


60 


.278 


180 


.46 


109 


.86 


58 


.28 


179 


.47 


106 


.88 


57 


.282 


177 


.48 


104 


.9 


56 


.284 


176 


.49 


102 


.92 


54 


.286 


175 


.5 


100 


.94 


53 


.288 


174 


.51 


98 


.96 


52 


.29 


172 


.52 


96 


■.98 
1. 


51 

50 



284 



COTTON MANUFACTURE. 



KOVESTG TABLE 



Showing the size of roving from No. .05 to No. 8, by 
the weight of 12 yards, in grains. 



Number 


Grains. 


Number. 


Grains. 


Number. 


Grains. 


Number. 


Grains. 


.05 


2000 


.108 


926 


.185 


541 


.8 


125 


.052 


1923 


.11 


909 


.19 


526 


.85 


118 


.054 


1852 


.112 


893 


.195 


513 


.9 


111 


.056 


1786 


.114 


877 


.2 


500 


.95 


105 


.058 


1724 


.116 


862 


.205 


488 


1. 


100 


.06 


1667 


.118 


847 


.21 


476 


1.05 


95 


.062 


1613 


.12 


833 


.215 


465 


1.2 


83 


.064 


1563 


.122 


820 


.22 


455 


1.25 


80 


.066 


1515 


.124 


806 


.225 


444 


1.3 


77 


.068 


1471 


.126 


794 


.23 


435 


1.35 


74 


.07 


1429 


.128 


781 


.235 


426 


1.4 


71 


.072 


1389 


.13 


769 


.24 


417 


1.5 


67 


.074 


1350 


.132 


758 


.245 


408 


1.65 


61 


.076 


1316 


.134 


746 


.25 


400 


1.8 


55 


.078 


1282 


.136 


735 


.275 


364 


2. 


50 


.08 


1250 


.138 


725 


.3 


333 


2.25 


44 


.082 


1220 


.14 


714 


.325 


308 


2.75 


36 


.084 


1190 


.143 


699 


.35 


286 


3. 


33 


.086 


1163 


.146 


685 


.375 


267 


3.5 


29 


.088 


1136 


.149 


671 


.4 


250 


4. 


25 


.09 


1111 


.152 


658 


.425 


235 


4.5 


22 


.092 


1087 


.155 


645 


.45 


222 


5. 


20 


.094 


1064 


.158 


633 


.475 


211 


5.5 


18 


.096 


1042 


.161 


621 


.5 


200 


6. 


17 


.098 


1020 


.165 


606 


.55 


182 


6.5 


15 


1 


1000 


.169 


592 


.6 


167 


7. 


14 


.102 


980 


.173 


578 


.65 


154 


7.5 


13 


.104 


962 


.177 


565 


.7 


143 


8. 


13 


.106 


943 


.181 


552 


.75 


133 







SPESTNING. 



285 



YAEN TABLE, 



Showing the size of yarn from Ko. 1 to ISTo. 120, by the 
weight of one hank in grains. 



No. 


Grains. 


No. 


Grains. 


No. 


Grains. 


No. 


Grains. 


No. 


Grains. 


1 


7000 


25 


280 


49 


143 


73 


96 


97 


72 


2 


3500 


26 


269 


50 


140 


74 


95 


98 


71 


3 


2333 


27 


259 


51 


137 


75 


93 


99 


71 


4 


1750 


28 


250 


52 


135 


76 


92 


100 


70 


5 


1400 


29 


241 


53 


132 


77 


91 


101 


69 


6 


1167 


30 


233 


54 


130 


78 


90 


102 


69 


7 


1000 


31 


226 


55 


127 


79 


89 


103 


68 


8 


875 


32 


219 


56 


125 


80 


88 


104 


67 


9 


778 


33 


212 


57 


123 


81 


86 


105 


67 


10 


700 


34 


206 


58 


121 


82 


85 


106 


66 


11 


636 


35 


200 


59 


119 


83 


84 


107 


65 


12 


583 


36 


194 


60 


117 


84 


83 


108 


65 


13 


538 


37 


189 


61 


115 


85 


82 


109 


64 


11 


500 


38 


184 


62 


113 


86 


81 


110 


64 


15 


467 


39 


179 


63 


111 


87 


80 


111 


63 


16 


438 


40 


175 


64 


109 


88 


80 


112 


63 


17 


412 


41 


171 


65 


108 


89 


79 


113 


62 


18 


389 


42 


167 


66 


106 


90 


78 


114 


61 


19 


368 


43 


163 


67 


104 


91 


77 


115 


61 


20 


350 


44 


159 


68 


103 


92 


76 


116 


60 


21 


333 


45 


156 


69 


101 


93 


75 


117 


60 


22 


818 


46 


152 


70 


100 


94 


74 


116 


59 


23 


304 


47 


149 


71 


99 


95 


74 


119 


59 


21 


292 


48 


146 


72 


97 


96 


73 


120 


58 



286 corroN manufacture. 



EXPLANATION OF THE KEED TABLE. 

1. Manchester, Stockport, and the United States count 
by the number of ends in one inch. 

2. Bolton counts by the number of beers on 24^ inches, 
20 dents to a beer. 

3. Blackbiu'n counts by the number of beers on 45 
inches, 20 dents to a beer. 

4. 6-4thB, Preston, counts by the number of beers on 
58 inches, 20 dents to a beer. 

5. 9-8ths, Preston, counts by the number of beers on 
44 inches, 20 dents to a beer, 

6. 4-4ths, Preston, counts by the number of beers on 
39 inches, 20 dents to a beer. 

7. 7-8ths, Preston, counts by the number of beers on 
34 inches, 20 dents to a beer. 

8. l!^ankeen counts by the number of beers on 20 
inches, 19 dents to a beer, 

9. Scotch and Carlisle count by the number of dents 
on 37 inches. 

Goods shrink about -^ in bleaching or finishing. 

The following table shows at a glance the number 
of dents in an inch, and the corresponding count of 
reed. 



EXPLANATION OF THE REED TABLE. 287 

The first column contains the number of dents in one 
inch, opposite to which are the counts of the reeds accord- 
ing to the system of counting. 



288 



COTTON MANTJFACTUEE. 



li 

go 


Ot-'*T-tG0»O(M(3i'X>C0Ot-'+li-(Q0i0<M 

t-t-OOGOOOOiOiOiOOTHT-t-i-ICqoiCNCO 
tHt—It— It— (t-ItHt— iT—trH 


1 


lO lO T-H CO tH CO C^ t- CM t- CC GO CO Oi ■* Oi 
O rM rH C^ C>J CO CO -* 'rf^ O lO CO CO t-; b^ CO GO 

tA cm" Co' '*" lO CO t-^ GO* OJ O i-H C^ CO -* IQ CO* t-^ 

(yi<?i<?^(Mc^<M<?ic^(?icocococococococo 


g 



1 


O^ lO t-; en lO t-; <>1 lO t-^ (M lO t-- 

oi^oiT-H*^cdGO*ocoid-fc-^aJa^-^*coGdTH 

^';tf'*^OiOlOCOCOCOCOCDt-t-4>»t^OO 


|2 


t- 'tH T-J GO lO Ol O:' CO CO ^ "* '^, "^ *^ <^ 
^ O* t-^ Ci O* S^ ^* O* t-^ ci rH CM* -** CO* t^ Oi r-5 
COCOCOCO^-*'*'*^-^iOlOlO»OlOiOCO 


SS , 
II 


C3iOiOOQqt-;t-;COt-K:>lO^':}HCOCOCM<M 

Oi O* CM* ^* CO* GO* O CM '*" CO GO O CM -H* CO GO O 
CO-rH'^-^-'^-^iOiOlOiOiOCO'lOCDCOCOl^- 




(M-xHcocx) cM'!^^coco cm^^cogo cm 

^COGOOcM'lOt-^crirHCOCOGOOCM^lr^aJ 
-rH^^iOiOiOiOlOCOCOCOCOt-tr-t-t-t- 




OiGOt^COiO-^COCMrH CiOOb-COXO-^ 
C» O CO* CO* Oi CM* lO* GO* rH* '^ t- ai CM id GO rH* ^ 
lOCOCOCOCOt^t-t-GOGOOOGOO:)CiOiOO 

T-l tH 


1 

n 


lOCOt— GO THCMCOiOCOt— GO CMCOlO 
(M'^COCXJiHCOOt-Cjir-JCOiOoq-rHcM^^CO 

TH*idcot-^aJOTHcMco»o*cdt-^oo*Oi-H(Mc6 

(MCq<MCM(MCOCOCOCOCOCOCOCO-*^-^^ 


Manchester, 

Stockport, 

and 

United States. 


OCM^COQOOCM'^ICDGOOCM^COOOOCM 
■^TjH'rH^^lOlOiOiOiOCOCOCOCOCOlr^t- 


No. of 

Bents in 

one 

inch. 


OrHOICO-^OCOt-OOOlOrHCMCO^lOCO 
CMCM(M<M(MCM(M<M<MCMCOCOCOCOOOCOCO 



lO lO 


iO lO 


lO 


lO lO 


CM >0 t- 


OT lO t- 


OT lO t- 


OT lo ^^- 



KEED TABLE. 289 



Ci':CCOO^,~-^THGOlO<?^OiCC>COO^-'5i^THOO^OO^Oi':OCOO 
CO O -+ O) T-l O Oi -^-J O O CO 1-^ T-H O CO Ol CO O Ot) -t- O -* CO G<1 
CO -* -H -H lO O iO O ■:© tr- t- t- QO -X) CO Cfi O o5 O' O r-H rH T-H C>T 
1— ItHt— (t— IT— IrHTHr-ti— It— IrHrHi— ti-HT-I^T-ii-lG<lCMCMC<)(?^CM 

'^ lO lOi— (COTHOCMt'-O^t-COt-O^C/D^ lO lO 

o O' 1— I th c^^ :m CO CO '^ ^ lo o ^ ■:o i^ i^ CO o:> C55 o t— i r— ■ 
00 c; i-H oi co' -^' id iiD i>^ .6 ci o th oi oo --t^ o* '-^ t- co o th ot co' 

CO-NH^-:H'*-^^':H-+l^^iOKt.OOiOiOiO>OiO<:OCD<:OCO 



lO lO »0 lO 
G<l lO t^ CT lO t-. 

co"idi>^0(>i^<:da^i-lcooaooG^-^t^CDrHco'<:oo6oG^*io 

GOG000050iOi050SOOOOi-HT— ItHtHt— ICMO^OICMOOOOCO 



Cti O OO .t- ^1— ICZii-OCMOlOCO t^'rHr-IOOiOO^OiOCO 

(>i -^ O 00 oi 1-^ CO "^ i:© GO oi rH CO O CO go" O tH" CO id 1:0' 00 o O^ 

<X)<©ccl':oco^^-J^-l^-t-^^-^^-oocoooQOooOiOiOiCiCia500 



VOiOiOiOlOiOiOlOiOiOlOlO 

T-Hr-JO CiOiOOGOt^t-COCOOlO'TtH'^C-OOOOqcMrHi— 10 

o-i "^ CO GO aJ 1-5 co' id t-^ ci th CO o" t^ oi -rH co' o t-^ ci th co' id t- 

t-t-t^-b-t-QOGOGOGOCOOiaiOiOiOiOOOOO'-'THr-li— I 



T^COOq OT'-HCOC» oi^coco cm-hcoco C^^-rt^COCO 

th CO id Qo o OT ■^' o as th 00' id t-^ o oi h^' cd go tH co' id i-^ oj -ri 

GOGOGOGOCSOiOiCiOiOOOOrHTHrHT— I— ICMOqCJ-TO^CMOO 



CO CNrH" OSCOt^COlO'rHCO CM rH aiOOfc^COlO-=^COOTr-J 

i--^o'co'coa)rH^'tr-^ococdcicMiOGo'i-5-^i>^Ci(MidQ6i-5-+i 
Ot— (tHt— lTH(^"^<MG■:^cocococo■^^^-+ll.OlOlOlO<:ococot^t:^ 



COt^GO 1—1 COiOCO— IGO i-ICMCO'^iOCDC5i iHCOCOlO 

GoocMOt-^Oii— lcolO^:-G5c^^'*':Dooo(^^ri^cooiTHcolO^-- 
'*cdt-^Goaio(>^cd'*'ld<:OG6a^cdTHco^ldcdJ~~^aio1-HC^ 

■*-+!-*. '^•^iOlOiOiOiOiOiOiOCOCO<X>COCOCOCOCOi^t-t^ 



'*COQOC;'(M-dH<:OOOOCM^i:CCOOG<l-THCOGOOCM'*COQOO 
I:-!,— -t-GOCCCOGOOOCiOiOiCiOiOOOOOr- 11— 11— IrHi— l(M 



l^-GOOSOi-HCMCO'+liOCOt-GOOlOi— l(M00-rHl-0C0t-00C:5O 
OOCOCO-^^-^-^-rfl^-tl^^H^lOiOiOlOlOiOlOlOiOiOCO 



13 



290 corroN ihanufactuke. 



LINEN YARN TABLE, 

Showing tlie weight of one lea, or cut, in grains, from No. 
1 to N"o. 200. 

The first cohimn is the number of the yarn, opposite to 
which is the weight, in grains, according to the length 
weighed, which, in the table, is one cut, or 300 yards. 

One lea, or cut, of linen yarn contains 300 yards, and 
one pound avoirdupois contains 7000 grains troy ; hence, 
the yards in one cut are to the grains in one pound, as 
300 is to YOOO, or 3 to 70. 

To find the nuiriber. 
Multiply the length in yards by 70, and divide their 
product by the weight, in grains, multiplied by 3. 

Excmiple. 
If 2400 yards weigh 7000 grains, what is the number ? 

Worked out hy Cancellation. 



1-7(000 
1-3 



24(00-8 
7(0-1 



Answer. 



The same without Cancellation. 
Dividend 2400x70 



Divisor 7000 x 3 

Answer. 



LIA^EN YAKN TABLE. 291 

How many yards are there in one pound of l^o. 8 ? 

Worked out hj Cancellation. 
7000400 
8 
1-70 3 



100 X 8 X 3 =^ 2400 

Answer. 



The sa/me without Oa/riGellation. 

Dividend Y000x8x3 _ ^^qq 

Divisor 70 

Answer. 



What is the weight of 2400 yards of Ko. 8 ? 



Worked out hy Cancellation. 



1-8 
1-3 



2400-800400 

70 



100 X 70 ^=: 7000 grains, or one pound. 

Answer. 

The same without Cancellation. 

Dividend ...... 2400x70 ^^^^ 

= 7000 grams. 

Divisor 8x3 

Answer. 



292 



COTTON MANUFACTURE. 



LINEN YARN TABLE, 



Number. 


Grains. 


Number. 


Grains. 


Number. 


Gra'ns. 


1 


7000 


20 


350 


115 


61 


2 


3500 


25 


280 


120 


58 


3 


2333 


30 


233 


125 


56 


4 


1750 


35 


200 


130 


54 


5 


1400 


40 


175 


135 


52 


6 


1167 


45 


156 


140 


50 


T 


1000 


50 


140 


145 


48 


8 


875 


55 


127 


150 


47 


9 


778 


(iO 


117 


155 


45 


10 


700 


65 


lOS 


160 


44 


11 


636 


70 


100 


165 


42 


12 


583 


75 


93 


170 


41 


13 


538 


80 


88 


175 


40 


14 


500 


85 


82 


180 


39 


15 


467 


90 


78 


185 


38 


16 


438 


95 


74 


190 


37 


IT 


412 


100 


70 


195 


36 


IS 


389 


105 


67 


200 


35 


19 


368 


110 


64 







WOESTED AND WOOLLEN YARN TABLE. 293 



WORSTED AND WOOLLEN YARN TABLE, 

Showing the weight of one hank, in grains, from 'No. 1 
to No. 200. 

The first column is the number of the yarn, opposite to 
which is the weight in grains, according to the length 
weighed, which, in the table, is one hank, or 560 yards. 

One pound avoirdupois contains 7000 grains troy, and 
one hank of woollen yarn contains 560 yards ; hence, the 
yards in one hank are to the grains in one pound, as 560 
is to YOOO, or U to 1Y5. 

To find the number. 
Multiply the length in yards by 1T5, and divide their 
product by the weight in grains multiplied by 14. 

Example. 
If 5600 yards weigh one pound, what is the number? 

Worked out hy Cancellation. 



147.5-70(00 
144 



56(0044 
17540 



10 Answer. 



The same without Co/ncellation. 
Dividend 5600 x 175 



= 10 



Divisor 7000x14 

Answer. 



294 COTTON MANUFACTUEE. 

What is the weight of 5600 yards of No. 10 ? 
Worked out hy Cancellation. 



1(0 
144 



560(040 
1Y5 



175 X 40 1= YOOO grains, or one pound. 

Answer. 

The same without Ca/noellation. 
Dividend . . . . 5600 X 175 ^^QQQ^^^.^^^ 

Divisor 10x14 

Answer. 

How many yards are there in one pound of IS'o. 10 ? 

Worlisd out hy Cancellation, 
7000-200 



1-35475 



10-2 
14 



200 X 14 X 2 ^ 5600 

Answer. 

The same without Ca/ncellation. 
Dividend 7000x10x14 



5600 



Divisor 175 

Answer. 



WOESTED AND WOOLLEN YARN TABLE. 



295 



WORSTED AND WOOLLEN TARN TABLE, 

Showing the weight of one hank, in grains, fi'oni No. 1 

to 'No. 200. 



Number. 


Grains. 


Number. 


Grains. 


Number. 


Grains. 


1 


7000 


20 


350 


115 


61 


2 


3500 


25 


280 


120 


58 


8 


2333 


30 


233 


125 


56 


4 


1750 


35 


200 


130 


54 


5 


1400 


40 


175 


135 


52 


6 


1167 


45 


156 


140 


50 


7 


1000 


50 


140 


145 


48 


8 


875 


55 


127 


150 


47 


9 


778 


60 


117 


155 


45 


10 


700 


65 


108 


160 


44 


11 


636 


70 


100 


165 


42 


12 


583 


75 


93 


170 


41 


13 


538 


80 


88 


175 


40 


14 


500 


85 


82 


180 


39 


15 


467 


90 


78 


185 


38 


16 


438 


95 


74 


190 


37 


17 


412 


100 


70 


195 


36 


18 


389 


105 


67 


200 


35 


19 


368 


110 


64 







296 



COTTON MANUFACTURE. 



KAILWAY-IIEAl). 

WITH DEArER's PATENT EVENER ATTACHED. 

The following tables and remarks were furnished by Mr. 
(ieorge Draper, Hopedale, Mass : 

Below I give a table showing the actual result of the 
use of the Eveners in the Boott Cotton Mills at Lowell, 
from July 19 to August 4, 1866. The drawing from each 
of the heads was weighed carefully over 150 times. The 

Table of Weights where the Evener avas Used. 









73 


74 


75 76 


77 


78 


79 


80 


81 


82 


83 


84 


85 


86 


87 


88 




1 


















3 




































1 


1 




1 
































2 




1 






































1 


1 


1 
























— 











1 
1 


2 

4 


3 
2 


3 

5 


1 


2 
















— 











1 




4 


1 


2 


^ 


2 


1 































































— 


— 


1 


1 


4 

2 


3 


3 


1 
1 


1 

'Y 


1 


































1 


^r 


fi 










































9, 




4 


1 


2 


1 



























E 


1 


2 


1 

1 
2 


4 


2 
2 
1 


3 
3 
2 


1 

3 


1 


1 






























1 


2 


1 


1 


8 


2 








































— 


1 

1 


4 
3 


1 


3 
3 











































2 


2 


16 


20 


17 


31 


25 


30 


9 


3 


1 













EAILWAY-HEAD- 



297 



Standard aimed at was 79 grains (between the Hack lines) 
for a given length. The drawing was straightened out, a 
strip of board laid on, and the di-awing cvit off at each 
end with a sharp knife, and then carefully weighed. Mark 
the result — any weighing not varying more than 4 or 5 
grains from the standard, either way, would make com- 
paratively Kttle difference. That weighing 72 in number 
20 yarn, would vary one number one way, and 83 one 
number the other way. That with the Evener in weigh- 

Table of Weights where the Evener was not used. 









73 


74 


75 


76 


77 


78 
2 


79 


80 


81 


82 


83 


84 


85 


86 


87 


88 











— 










1 


1 







1 


1 


~F 







1 

























1 


1 


















1 






















2 


1 


1 


2 


1 


2 


2 


1 


























1 




1 


3 




1 


4 








1 


















— 


1 





1 
1 


1 

2 
1 


1 
1 




2 
1 


1 


2 

1 


1 


1 
3 


2 
3 
2 





1 
1 


— 


. 



















2 


2 






3 


1 


~T 


1 


T 


3 


1 






1 




















1 






3 




1 


3 








1 













































■ 














— — 






— 


1 


2 




1 


3 


— 


2 
2 


2 


2 





1 







1 


~ 








1 






— 




~T 


1 


2 


2 




2 
1 


1 





1 


— 


1 


1 





1 












— 




— 


1 

2 


2 
1 





~2~ 


1 
1 


T 




1 


1 



























2 


5 i 11 


20 


12 


16 


20 


14 


13 


9 


8 


12 


4 


4 


2 


1 1 





298 COTTON MANUFACTURE. 

ing 156 times in three weeks, varied more than that only 
4 times, 2 times Y3 and 2 tinfes 74. ]^ow look at the 
other weight at the same time, and under the same circum- 
stances, excejpt the Evener. Out of 153 weighings, that 
weighed 75 — 7 times and more than 83 — 23 times. The 
one with the Evener weighed right, or within one grain 
of right, 86 times, while the one without the Evener did 
but 50 times. In one the weighings are between 73 and 
83 — in the other scattered from 73 to 88. 

]Sr. B. — The above is by some called Hayden & Wyllys' 
Patent Evener. 



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AGENCY. 



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No. 4 MRKET SQUAHE, Bank of Commerce Building, 

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MANUFACTURER OP 



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Opposite the Worcester Passenger Station. 



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Being a Complete School for the Apprentice as well as the advanced Machinist, 
showing how to make and use every tool in every branch of the business; with 
a treatise on Screw and Gear Cutting. By Walter Fitzgerald, Inventor and 
Mechanical Engineer. 

Illustrated with plates. 1 vol. 18mo., cloth. 75 cents. 

Published and for sale by 

JOHN WILEY & SON, 

535 Broad-way, Nevr York. 



R U S K 1 N ' S WORKS 



UNIFORIIE IN size: AND STYLE. 



MODERN PAINTERS.— 5 vols., tinted paper, beveUed 

boards. Plates. Inbox $14 00 

Ditto. ditto. half calf 21 00 

Ditto. white paper, without plates . . . 9 00 

Ditto. ditto. ditto. half calf . , . 17 50 

bTONES OF YENICE.— 3 vols, on tinted paper, bevelled 

boards. In box 7 00 

Ditto. ditto. half calf 12 00 

MISCELLANEOUS WORKS— (including all the Volumes 
named below). 5 vols, on tinted paper, beveUed boards, 

in box 14 00 

Ditto. ditto. half calf . , , . 20 00 

SEVEN LAMPS OF ARCHITECTURE— 1 vol. 12mo., cloth 1 25 
Ditto. ditto. 1 vol. 12mo., plates, cloth . . 1 75 

LECTURES ON ARCHITECTURE AND PAINTING— 

1 vol. 12mo., cloth 1 60 

TWO PATHS— Being Lectures on Art. 1 vol. 12mo., cloth, 

plates 1 25 

ELEMENTS OF DRAWING— 1 vol. 12mo., cloth . . 1 00 
ELEMENTS OF PERSPECTIVE— 1 vol. 12mo., cloth . 1 00 
POLITICAL ECONOMY OF ART— 1 vol. 12mo. . . 1 00 
PRE-RAPHAELITISM— Construction of Sheepfolds— King 

of the Golden River. 1 vol. 12mo., cloth . . . I 00 
SESAME AND LILIES— Two Lectures on Books and 

Women. 1 vol. 12mo., cloth 1 00 

LECTURE BEFORE SOCIETY OF ARCHITECTS . 
RUSKIN'S COMPLETE WORKS— 13 vols., tinted paper, 

bevelled boards 35 00 

Ditto. ditto. 13 vols, half calf . . , ,55 00 

BEAUTIES OF RUSKIN ; OR, THE TRUE AND BEAU- 
TIFUL— Selected from the Works of John Ruskin, by 
Mrs. L. C. Tuthill. 1 vol. 12mo., tinted paper, bevelled 

boards, gilt top 2 50 

Ditto. ditto. white paper, cloth . . . 2 00 

Ditto. ditto. half calf 4 00 

PRECIOUS THOUGHTS, MORAL AND RELIGIOUS- 
Selected from the Works of John Ruskin, by Mrs. L. 0. 
Tuthill. 1 vol. 12mo,, tinted paper, bevelled boards, gilt 

top 2 00 

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*^* Any of the above works will be prepaid by mail on receipt 
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valuable Scientific Works 

JOHN WILEY, 535 BROADWAY. 



3URGESS, N. G. THE PHOTOGRAPH ANI AMBROTYPE MANtJAL 
A Practical Treatise oi the art of taking Positive and Negative Photographs onPapei 
and Glass, &c. 1 vol. 18rao. Cloth. $1 00. 

FAIRBAIRN (WM.) C.E., E.R.S, ETC. ON THE APPLICATION OF 

CAST AND WROUGHT IRON TO BUILDING PURPOSES. 
1 vol. 8vo. Numerous cuts. Cloth. $2 00. 
" No engineer can do without ihis book." — Scientifio American. 

n.AND BOOK OF YOUNG ARTISTS AND AMATEURS IN OIL 

PAINTING; 
Buing chiefly a condensed compilation from the celebrated Manual of Bouvier, and 
other distingiii.shed Continental Writers on the Art. Adapted for a Text-Book, as well 
as for Self-luslniction. Appended — a new Explanatory and Critical Vocabulary. By 
an American Artist. 12mo. Cloth. $2 00. 

HATFIELD (R. G). THE AMERICAN HOUSE CARPENTER. 
A Treatise upon Architecture, Cornices, and Mouldings, Framing, Doors, Windows, and 
Stairs, etc. New, thoroughly revised and improved edition, with about 150 additioiir.) 
pages and numerous additional plates. 1 vol. Svo. $3 50. 
"Every House Carpenter ought to possess one of these books." — Journal of Gommerce, 

LESLEY (J. P.). THE IRON MANUFACTURER'S GUIDE, 
To the Furnaces, Forges, and K<dliug Mills of the United States, with maps ; to which 
IS appended a History of the Manufacture of Iron, a summary of the Statistics of the 
American Production of Iron, and a geological discussion of the Iron Ores of the U. S., 
by J. P. Lesley, Secretary of the American Inrn Association, and published by order oi 
the Board of Managers. 1 vol. Svo. $8 00. 
" Invaluable to every miner, manufacturer, and dealer of iron." 

REID'S VENTILATION IN AMERICAN DWELLINGS. 
With a Scries of Diagrams, presenting Examples in Ditferent Classes of Habitation. By 
David Boswell Keid, M.D., F.U.S.E., formerly Director of the Ventilation at the llousea 
of Parliament, London, etc., etc To which is added an Introductory Outline of the 
Progress of Improvement in Ventilation. By Klishia Harris, M.D., late Physician in 
Chief of the N. T. Quarantine Hospitals, ect., ect. 1 vol. containing about lOO 
diagrams col. and plain. $1 50. 

" We know of no book where in so brief a space, the best means of airing, wanning, 
and lighting buildings are so clearly set forth, a* in that we have just described." — Gin- 
■iinndti Gazette. 

SMITH (LIEUT. R. S.). A MANUAL OF TOPOGRAPHICAL DRAWING, 
By Lieut, li. S. Smith, U. 8. Army, Professor of Drawing in the U. S. Military Ac«deiiiy 
West Point. 1 vol. 8vo., plates, cloth. ^2 00. 

" We regard the work as a choice addition to the library of science and art, and one 
that has long been needed by the Professor." — R. li. Journal. 

SMITH (LIEUT. R. S.). MANUAL OF LINEAR PERSPECTn'E. 
i'erspective of Form, Shade, Shadow and llellection. 1 vol. 8vo. Plates. $2 f).'. 

" We do not remember to have seen a more complete and popular treatise on the Hub 
•Oct." — R. Ji. Journal. 

SMEB. ELEMENTS OF ELECTRO-METALLURGY. 
Bevlsed, corrected, and con.^idcrably enlar ;ed. Illustrated with Electrotypes aad 
numerous wood-cuts. 1 voL 12mo. 

WEISSENBORN (G.) AMERICAN ENGINi^ERING. 
Illustrated by large and detached Engravings, embracing various branches of Mechanicai 
irt, Sta.-oi. i.-y. Marine, and Locomotive Engines, Manufacturing Machinery, Printing 
'•resses, To-^lt., Grist, Steam. Saw, and Eolling Mills, Iron Buildings, &c., of the newest 
%iid most iiv\ Tovfcu constructif>n. $36 00. 



IMl'OKTANT MILITARY WORKS. 



MA HAN'S FIELD FORTIFICATIONS. 

t TREATISE ON FIELD FORTIFICATIONS; containing instructions en the Methods 
of Laying out, Constructing, Defending, and Attacliing lutrencbments. With the 
General Outlines, also, of the Arrangement, the Attack and Defence of Permanent 
Fortifications. Third Edition, revised and enlarged. By D. H. Mahau, Prof. U. S. 
Military Academy, West Point. 1 vol. Full cloth, with plates, $8 50. 

MAHAN'S ADVANCED GUARD AND OUT-POSTS. 

4N ELEMENTARY TREATISE ON ADVANCED GUARD, OUT-POST, AND 
DETACHMENT SERVICE OF TROOPS, and the Manner of Posting and Ilaudling 
them in the presence of an enemy. With an Historical Slvetch of tlie Rise and Progress 
of Tactics, &c., &c., intended as a Supplement to the System of Tactics adopted for the 
Military Service of Vnu United States, and especially for the use of Officers of Miliiia 
and Volunteers. By D. H. Mahan, Prof. U. S. Military Academy, West Point. 1 vol 
ISmo. Full Cloth, new edition, with plates, $1 25. 

REOOMMENDATIONS. 

Headquarters op the Army, 
Washington, Sept. 6, 1861. 

Dear Sib : 

I learn, with pleasure, that you propose issuing new editions of your 
works on ^^ Field FortiJicaUons" and" Oui-Fosts." The former I consider the 
best treatise on the subject in our language ; and the latter contains much, in a 
small compass, of high value to officers, volunteers, and others, in the present 
war. 

Yours very truly, 

WINFIELD SCOTT. 
Prof. D. H. Mahan, 
V. S. Ililifary Academy, West Point, J^. Y. 

The small volume of Prof Mahan, of the United States Military Aca- 
demjr, on Field Fortifications and some kindred subjects, contains most valuable 
information well digested and clearly set forth. It can be commended to the 
officers of volunteers, and all who desire such information, as containing, in 
moderate compass, a large amount of important mUitary knowledge. 

The little treatise on Out-Posts, &c., of the same author, also presents a 
subject of great interest, especially to Infantry and Cavalry Officers. 
Tours, 

G. TOTTEN, Br. Brig.-Gen. U. S. Ekg. 
Encmneer DeparTiMENT, Sept. 6, 1861. 



PUiiLISHED AND FOR SaLE BY 

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Joiin Riiskm^s Works, 

(UNIFOKM HKKIES). 

PUBLISH'^^.D BY JOHN WILEY, 535 BROADWAY. 



t.— MODERN PAINTERS. VOL. I— GENERAL PRINCIPLES OF ART 
&.nd Truth as an Essential Element. $2 00. 

"A very extraonlinary and delightful book, full of truth and goodness, of T)Ower anc 
Deauty." — Marth British Revimo. 

VOL. II.— TRUE IDEAS OP BEAUTY. 

Price, %\ 00. 

" Mr. Euskin's work will send the painter more than ever to the study of nature ; will 
train men who have always been delighted spectators of nature, tc be also attentive 
observers. Our critics will loarn to admire, and mere admirers will learn how to criti- 
cise ; thus a public will be educated."— j6?acA;'icood's Magazine 

VOL. III.— STYLE, EINISH, LANDSCAPE, ETC. ; 



With cuts and eighteen illustrations, drawn by the author. $2 60. 

"This book may be taken up with equal pleasure whether the reader be acqnalnt«a m 
not with the previous volumes, and no special artistic culture is necessary In order tf 
snjoy its excellences or proflt by its suggestions." — Westminster Remienn 

VOL. IV.— MOUNTAIN BEAUTY. 
With numerous cuts. $2 00. 

2.— THE SEVEN LAMPS OP ARCHITECTURE. 
I vol. With Fourteen Etchings, by the author. $1 75. 

"The politician, the moralist, the divine, will find in it ample store of instructive 
nutter, as well as the artist." — Exaininer. 

3.— THE STONES OF VENICE. 
Illustrated by numen ns w'ood-cnts from Drawings bv the Hiunor. 3 vols. $7 00. 

"No one who has visited Venice can read this book without having a richer glow 
thrown over his rcmembrauces of that city, and for tho.se who have not, Mr. Kuskin 
paints it with a firmness of o\itline and vividness of colouring that will bring it before 
the imagination with the force of reality." — Literary gazette. 

4.— PRE-RAPHAELITISM, AND NOTES ON THE CONSTRUCTION OF 

SHEEPFOLDS. 
In 1 vol. $1 00. 

" There is much to be collected from it which it is very important to remember." — 
Q-aardian. 

5.— LECTURES ON ARCHITECTURE AND PAINTING. 
Delivered at Edinburgh in Nov. 1853. 1 vol. 12nio. With fifteen Illustrations on tinted 
paper, after Drawings by the author. $1 60k 

6.— THE ELEMENTS OF DRAWING. 
In Three Letters to Beginners. 1 vol. Plates. $1 00. 

"We close this book, feeling confident that no student of Art should launch forth 
irithout this work as a compass in the binnacle." — AthenopMm. 

7.— THE POLITICAL ECONOMY OF ART; 
<eing the Subject (with additions) of two lectures delivered at Manchester, July, 1857 
vol. $1 00. 
" It is needless to criticise or commend the works of Kuskin." — N. Y. Observer. 

S.— THE BEAUTIES OF RUSKIN; 
in, the True and the Beautiful in Nature, Art, Morals, and Keligion. Selected from th« 
works of John Ruskin, with a notice of tho author. By Mrs. L.'C. Tuthill. 1 vol. .$2 0<i. 
This elegant volume, though coiuposed only of C5:tiacts, has been so handled, as to 

f)osses8 all the interest of a continuous work on Art, etc., arr.angcd in chapters, without 
t« technicalitios, making it an agreeable com])anion to the Drawiug Uoom. 

" The author is an enthusiast, and inspii es the reader with his own intense love for Ui« 
True and the Good. It would be well to make this work a stidy La schoola u. 
•wlleges."— iV. y. Observer, 



Downins's and other AsricuUiiral Worb 

PUBLISHED IJY 

JOHN WILEY, 535 BEOADWAY. 



DOWNTNG, A J. TlIK FRUITS AXD FRUfT TRKKS OF AMKRICA, 

Of, the Culture, Propagation, and ManaKement in the Garden and Orcliard of Fruit 
Trees generally; vvitii ilescripliuns of all the finest varieties of fruit, native and forjiffa 
cultivated In this country. New edition, tboroiighly revised, with very large addiUoaa, 
especially in apples and pears. Edited by Charles Downing, Esq., brother of tbo l»tc 
A. J. Downing. One vol. 12iiio., containing over 750 pages. .$3 00. 

'■ No man who has a plot of 50 feet sqtiave should be without tins book ; while U, the 
owner of acres it is beyond all price." — Neiolnifgli Gdsctte. 

'•This book is, therefore, in our opinion, the very best work on Fruits that we have."— 
A meriuan A'jriouUiirist. 

" We hail the present work as the best American Fruit Book extant." — Ohio CuUi 
vator, 

DOWNING, A. J. COTTAGE RKS'DKNCKS: 

A Series of Designs for Rural Cottages and Cottage Villus, ami their Gardens and Grounds^ 
adapted to North America. Illustrated by nuinerous engravings. Third edition. Svo. 
Cloth. $3 00. 

" Here are pleasant precepts, suited to every scale of fortune among us; and general 
maxims which may be studie<l willi almost equal profit by the householder in the crowd 
ed city and the man of taste who retires with a full purse, to embody hia own ideas of a 
rural home." 

ni. 
DOWNING, A. J. LINDLEY'S HORTICULTURE. 
With additions. One vol. 12mo. $3 00. 

DOWNING, A. J. LOUDON'S GARDENING FOR LADIES, 
&.nd Companion to the Flower Garden. By Mrs. Loudon. 12mo. Cloth. $2 00. 

DOWNING, A. J. WIGHTWIOK'S iilNTS TO YOUNG ARCHITECTS, 
Oaleulated to faoilitato their practical operation; with additional Notes and Hints to 
Persons about Building in the Country. Svo. Cloth. $2 00. 

PARSONS ON 'the ROSE. 
The Rose — Its History, Poetry, Culture, and Classification. With two large colored 
plates, and other engravings. In one voL 12mo. New edition, with additions. Cloth. 
|l 255. 

"This elegant volume, devoted to a suliiect of universal attractivenesi, and exLanstiug 
most of the learning wliich applies to it, deserves a wide pojmlarity." 

VII. 

KEMP ON LANDSCAPE GARDENING 

How to Lay Out a Garden. Intended as a general Guide in choosing, formh •<, or im- 
proving an estate (from a quarter of an acre to a hundred acres in extent), with teferenc* 
to both design and execution. By Edward Kemp, Landscape Gardener, Birkenhead 
Park. Greatly enlarged, and illustrated with numerous plans, sectirns, and sketches of 
gardens and iiiirden objects. 1vol. 12mo. Cloth. Gilt. $2 00. 

*Tliis is just llie book that t ousands want." — N. Y. Observer. 

" It should be in the hands of every one who laakes even the slightest prcten.sionf> to 
Gardening."— P^iZff. City Item. 

VII,. 

cl.\uss]':n. thic flax moveaient. 

Its Importance and Advantages ; with Directions for the Preparation ot Flai Cotton, »ud 
the Cultivation of Flax. By the Chevalier Claussen. 12mo. 12 cents. 

LIEBTG. PRINCIPLES OF AGRICULTURAL CHEmSTRT 
With special reference to the late researches nuide in Knglaiul. 1 vol. 12mo. Cloth. 60o 

**♦ Cnpies will he mailed to any ctddresx, amd jjrepaid. on the 7'eceipt of theprio* 
Ctu/iD and Societies iviU lie nupplied- with the v'orks/nr jir eirAwrs, at a discoutU. 



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